According to Catholicism, does Matthew 16:18 ("thou art Peter; and upon this rock I will build my church, and the gates of hell shall not prevail against it.") justify that the Catholic Church is the one true church?
The section "Of the Institution of the Apostolic Primacy in blessed Peter" of the First Vatican Council's Dogmatic Constitution on the Church of Christ (Pastor Æternus) quotes Matthew 16:18 and related verses:
We therefore teach and declare that, according to the testimony of the Gospel, the primacy of jurisdiction over the universal Church of God was immediately and directly promised and given to blessed Peter the Apostle by Christ the Lord. For it was to Simon alone, to whom he had already said: 'Thou shalt be called Cephas,' [St. John 1:42] that the Lord after the confession made by him, saying: 'Thou art the Christ, the Son of the living God,' [St. Matthew 16:16] addressed these solemn words: 'Blessed art thou, Simon Bar-Jona, because flesh and blood have not revealed it to thee, but my Father who is in heaven. And I say to thee that thou art Peter; and upon this rock I will build my Church, and the gates of hell shall not prevail against it. And I will give to thee the keys of the kingdom of heaven. And whatsoever thou shalt bind on earth, it shall be bound also in heaven; and whatsoever thou shalt loose on earth, it shall be loosed also in heaven.'[St. Matthew 16:17-19] And it was upon Simon alone that Jesus after his resurrection bestowed the jurisdiction of chief pastor and ruler over all his fold in the words: 'Feed my lambs; feed my sheep.' [St. John 21:15-17] At open variance with this clear doctrine of Holy Scripture as it has been ever understood by the Catholic Church are the perverse opinions of those who, while they distort the form of government established by Christ the Lord in his Church, deny that Peter in his single person, preferably to all the other Apostles, whether taken separately or together, was endowed by Christ with a true and proper primacy of jurisdiction; or of those who assert that the same primacy was not bestowed immediately and directly upon blessed Peter himself, but upon the Church, and through the Church on Peter as her minister.
St. Robert Cardinal Bellarmine, the greatest Doctor of ecclesiology, wrote a De Romano Pontifice or On the Roman Pontiff (part of his De Controversiis or On the Controversies series) in which he shows—in more detail, against the errors and heresies of Calvin, Luther, et al.—how the above scriptural verses support the papacy.
source: this answer to the question "What is the origin of the Catholic Pope in the Bible?"
Wikipedia's Four Marks of the Church ...
one, holy, catholic and apostolic
... links to One true church which purports to outline the Roman Catholic doctrine -- 7 paragraphs with 15 footnotes which I won't copy-and-paste here.
That does mention "Peter" four times, including,
The Church recognizes that in many ways she is linked with those who, being baptized, are honored with the name of Christian, though they do not profess the faith in its entirety or do not preserve unity of communion with the successor of Peter.
I'm pretty sure it's also Catholic doctrine that "the Church" isn't "the church" -- it isn't the buildings.
Other relevant Wikipedia articles,
This (personal history or belief) may be off-topic here, I don't know. My Dad was born an atheist in England, and joined the Catholic (not the Anglican) church as a young adult -- he was or became a professor of Roman History and told me once that his choice of church was based on his view of history -- i.e. the continuity of Apostolic succession -- I think that is or was an example of "Catholicism" ... and not just his, I presume that Catholics would have taught him that view.
I suspect, I don't know, that doctrine as it's taught or emphasised might have changed in the last 50 or 60 years or so. When I was young (in Ottawa) the Catholic catechism I was taught, as far as I remember, included "If you're not baptised (and into the Catholic church at that) then you can't possibly go to heaven" -- which seems to me incompatible with what would have at that time been very recent doctrine, Lumen gentium which was 1964 (see also the last quote above which was from ibid.):
In addition, the Church declares the possibility of Salvation for non-Christians and even non-theists
You might find this relevant too: