Well, I don't know the conclusions drawn from these comments by the person you are citing, but in and of themselves, these comments do not support that idea, no. Does this writer actually argue this explicitly? The conclusions they do support are part of the position I have put forth before, namely, Religious and CV's are similarly consecrated by God and espoused to Christ but they live this reality out differently in most cases due to differences in context, charism, mission, etc. Most fundamentally, one group lives it out as consecrated religious and the other as consecrated secular persons. Beyond that, one group (ministerial religious) ordinarily lives it out implicitly while the other group (CV's living in the world) do so, and are meant to do so, explicitly. (Cloistered religious may do so more explicitly and some apostolic religious also legitimately feel called to do so.)
The profession of evangelical counsels effectively separates persons from or significantly qualifies their relationship to the world in fundamental areas (i.e., those of economics, power, and relationships). These religious may or may not be called to witness primarily to espousal per se; instead they may be called to live out this espousal in ways which make something else more directly the gift they bring to the Church and world. For instance, the Sisters of Mercy are consecrated Religious, espoused to God, etc, but the charism they specifically bring to Church and world is the gift of ministering Christ's mercy to the poor, marginalized and ignorant with a special vow for that. Espousal to God in Christ in an underlying and foundational reality which is usually left implicit in this as they act as spiritual mothers and sisters to the world of the marginalized and poor. In other words, for ministerial religious, their commitment to others often tends to move espousal per se to the background even as it moves the resulting gifts associated with spiritual motherhood and sisterhood to the fore. The gifts and graces of spiritual motherhood and sisterhood however, stem from their espousal/consecration which is itself a specification of their baptism.

Especially, neither does the difference in emphasis of the Rite of Profession of Religious from the Rite of Consecration under c 604 indicate one rite refers to espousal while the other does not. Nor does any difference refer to a different degree of espousal any more than this difference refers to a different degree of consecration. Again, one rite refers to the espousal of Religious who live out their consecration in terms of public vows and (diocesan hermits excepted) life in community, while the other refers to the espousal of virgins living exhaustively consecrated AND secular lives where their identity as Brides of Christ is explicit and the fundamental ecclesial gift they bring to the Church and world.
I think the passage you have cited says as much. What it does not (and cannot honestly) say is that the Bridal imagery or nuptial import is absent in the Rite of Profession/Consecration of Religious, nor that where it is present it is different in kind or degree from that of the Consecration of Virgins living in the world or vice versa. What differs is emphasis and context, charism and mission. Both Rites use Bridal language while the insigniae given in Religious Profession and the Consecration of Virgins living in the world is the same as has always been the case in any consecration and/or profession. These are nuptial in nature: veils, rings, etc. (Cf, for instance the picture and prayer of the giving of my own ring where the Bishop said, according to the prescribed rite: [[ Sister, receive this ring for you are betrothed to the eternal King: Keep faith with your Bridegroom so that you may come to the wedding feast of Eternal joy.]] So again, in both cases -- Religious and CV's living in the world -- espousal is real and fundamental. Where these two groups differ is in the way they are called by the Church to live this out and symbolize it for others.
Attempts to Deny the Nuptial Reality of Religious Profession
Though what you have cited does not say so, there is indeed a movement afoot (possibly only composed of a minority of CV's) to say that CV's under c 604 have the right to be called Brides of Christ where Religious do not. One CV actually (and erroneously) wrote that she has the right to ask a Sister calling herself a Bride of Christ to stop doing so! But the Church herself has traditionally understood her own identity as reflective of a spousal bond and vocation and has Traditionally recognized a special expression of that spousal bond and ecclesial identity in the vocations of Religious women and men. There is absolutely no indication that by reprising the secular vocation of canon 604 the Church wishes to affirm that CV's are Brides of Christ while denying Religious are similarly espoused. The evidence is quite the contrary in fact.
Additionally, some CV's have actually asserted that if Religious Women and Men share in the charism of spousality it weakens or dilutes the charism of CV's! Of course since we (Christians) are ALL ultimately called to this espousal and since the Church herself is the Virgin Bride of Christ, it hardly makes sense to argue that a lack of exclusiveness "dilutes" the CV's charism. ALL vocations, and especially all ecclesial vocations share in and express this universal conjugal love between God and his own. Relative to other vocations Religious and CV's image this universal vocation in a more explicit way even if they differ from one another in degree of explicitness, just as those called to marriage and the holiness and sacramentality of sexual love image different dimensions of this same universal call.

Additional Reasons for this Denial:
I think there are a couple of other related reasons as well. First, this minority of CV's seem to be impatient with the Church's (meaning here the whole People of God's) slowness in coming to understand and appreciate this "new" vocation. Admittedly, it is sometimes frustrating to give oneself to a little-understood or appreciated vocation! This leaves the increased hiddenness of the CV's vocation to rankle with some CV's. Instead of allowing time for the Church as a whole to establish and reflect on the unique gift quality of a consecrated vocation lived in the world and the things of the world (and therefore living without distinguishing garb, title, vows, or insigniae beyond the wedding ring each CV wears), there seems to be a need to establish themselves as special and "set apart" in a way which also actually betrays the fundamental secularity and the charism of the vocation. We ought not need to suggest we are special merely in referring to what distinguishes us from other vocations; sometimes we are special because we share a charism with others while our mission in extending or mediating this charism to others is quite different.

Secondly, it seems to be the case that a number of CV's really desire to be Religious, but for some reason are unable or even unwilling to enter a congregation and move through all the steps and formation required. For that reason there seems to be a movement afoot to take a secular form of consecrated life and transform it instead into a quasi-religious form which simply lacks, "all the bells and whistles." In such cases, where the radical secularity of the vocation is actually denied, the common and usually misguided question, "Why didn't you go the whole way and become a nun?" actually has some cogency. Related to this is the too-facile distinction of Religious life from secular life in a way which treats secular life as less than truly devout, and certainly as not fitting to one who is consecrated by God. As I have written here before, today the Church is moving to reappropriate a more adequate notion of secularity, an understanding which is to be carefully distinguished from secularism and where, whether consecrated, ordained, or lay, persons can embrace the fact that they are called to live out lives of radical discipleship to Jesus in the world and in the things of the world precisely in order to call others to the same discipleship. CV's will especially call others to recognize that they too share in some way in the vocation of spousal union with God in the midst of secularity.
This means that CV's living in the world have actually been given a significant place in this dimension of the Church's mission. Paradox is often hard for people to appreciate or embrace but here CV's are called to embrace and live the paradox of consecrated or eschatological secularity. The Church seeks to hold these two things together as a piece of its own sacramental character; she consecrates virgins TRULY living in the world so that they might be icons of the Christian paradox where the divine is exhaustively revealed in flesh, the sacred is revealed in the ordinary and all of existence is called to be a living symbol of the reality of God's love which is poured out in the creation of ordinary life.
Can Consecration Ever be Undone?

At her consecration the CV is uniquely graced and made especially capable of receiving the graces associated with bridal, virginal, and maternal love proper to the Kingdom or Reign of God; at the same time she is made legally and morally responsible for receiving and living out these graces as best she can on behalf of others in accordance with Canon Law and the Rite of Consecration --- especially as a consecrated person and icon of the universal calling of the whole Church to be Bride of Christ. As with Religious who are consecrated by God at perpetual or solemn profession (this does not happen with temporary profession), the consecration per se cannot be undone; even so, what can be relinquished or undone are the legal and moral rights and obligations which attend and mark the CV's entry into the consecrated state of life.
Religious are dispensed from their perpetual vows in order to achieve this relinquishment. When dispensed in this way they do not cease to be consecrated but they are no longer consecrated persons in the Church. Since CV's have no vows they cannot be dispensed from them, but it does happen that CV's leave the legal rights and obligations enjoined on them with consecration and thus too, leave a state of life with its commensurate obligations, responsibilities, and public privileges and expectations. Such a CV does not cease to be consecrated, but she does cease to be a consecrated person (i.e., one in a public state of consecrated life) in the church. She ceases, in other words, to be an iconic figure in the way CV's living in the world are called to be.
Is Christ the Consecrated Virgin's "Husband"?
Another way of buying into extravagant and elitist ontological claims is by embracing the notion that Christ becomes the CV's "husband." I admit that I have never been comfortable hearing some use this term and I have become more uncomfortable with it as it is linked with increasingly elitist notions of the CV's consecration. We must always remember the analogical nature of our language when we are speaking of God; when the eschatological reality of the metaphor "spouse" or "Bridegroom" is replaced by the this-worldly legal and social term "husband" we are no longer taking significant care with our language or our theology. Further, we are talking about a change in Christ's own identity which is also exclusionary and I emphatically don't think we can do that.
Those who are espoused, betrothed, or (perhaps less appropriate linguistically) "wedded" to Christ become unique sharers in and witnesses to the CHURCH'S identity as Bride of Christ. We never say Christ is the Church's husband; it is simply not appropriate nor theologically accurate. We refer to him as the Bridegroom because it preserves the dimension of a real marriage which is not yet consummated or marked by home-taking. We do the same with CV's; the Church does so in all traditional, official, or authoritative documents referring to this vocation that I have seen. (See for instance par 18 of Pius XII's "Sacra Virginitas" where Pius carefully and consistently maintains the distinction between Christ as spouse and others as "husbands" --- even going so far as to speak of virgins as espoused to Christ and thus free of husbands!) Neither then do we say the Church (nor individual Sisters, Brothers (!), Friars (!), or CV's) are Christ's wives. Such language strips away the eschatological and ecclesial nature of the identity the CV or any of these others have accepted and makes claims of a spousal bond apparently ridiculous. I believe this usage is theologically naive and harmful to the actual witness the CV is meant to give.
To summarize then, because the vocation is ecclesial and makes the CV an icon of the Church's own identity, as well as because it is a share in an eschatological reality and points to a union which occurs in eternity when neither man nor woman will be given in marriage, it cannot make of Christ a "husband" in a this-wordly sense. Again, in Xtn theology we tend to keep the Scriptural language of espousal (Bridegroom, spouse, Bride) and eschew more common language of wife and husband in speaking of this dimension of consecration precisely to maintain the eschatological nature of the union and identity. (Again, refer to Pius XII's usage in Sacra Virginitas.) Taking care in this way might also prevent some of the extravagant and elitist claims we are seeing and hearing from some CV's. After all, I have called this vocation one of eschatological secularity; just as CV's cannot deny or diminish the secularity of it and be true to it, neither can they legitimately deny nor diminish its eschatological nature without betraying the vocation.
Is the CV really a Bride of Christ then? Yes, absolutely, but in a way which is representative, iconic, proleptic, and prophetic, rather than exclusive or elitist. The CV is a Bride of Christ in a sense which says, "I am what you are also called to be eschatologically, and I am this here and now so that you might know you are also called to this!" She is not a Bride of Christ in a sense which says, "I am a Bride of Christ and you consecrated Religious are not!" nor, "I am a Bride of Christ now and will be so in eternity in a way you will never be!" Instead, the CV consecrated under c 604 lives out the specifically ecclesial identity of Bride to the eternal Bridegroom in a particularly vivid and coherent way; she does so precisely so others may also do so (and aspire to do so) in the differing ways God calls them to share in this foundational ecclesial identity. The call and mission of CV's consecrated under c 604 is a tremendously significant ecclesial witness which serves the whole Church in reminding us of something fundamental which has been lost sight of, namely, the universal call to spousal love, the call of every person and God's Church as a whole to a union with God through Christ that is best seen as "nuptial."
Though I have focused on the nuptial character of this vocation, I should also say that this call is also profoundly significant in extending and clarifying the Church's new and evolving stances on secularity and mission! This too is part of its charism and a witness and challenge the world needs profoundly. This vocation reflects a form of "set apartness" which itself is only truly expressed when it is lived exhaustively within the culture; it is the "set apartness" proper to the Incarnation of the Word of God and to a Church whose very nature (like that of the God she worships and mediates) is missionary. The CV living in the world ministers and missions, not merely by going out to segments of the world preaching, teaching, healing, and so forth, but by manifesting the Kingdom of God here and now IN secularity --- albeit a wholly transformed secularity, an eschatological secularity proper to the "time" when God will be all in all.
Please also see: On Consecrated Virginity: the Nature of This Espousal