As much as I admire the attempt to prove God's existence in a new way, this argument does not work.  The theists must be their own worst critics; that is, if what Mr. Vincente is really theism.  One interpretation of this argument is that God is to be seen as the totality of true propositions in a way that brings to mind Spinoza, Schelling and Hegel.  If this is not to be the interpretation, then there is a lot of question begging going on, but in any case, let us look at the argument premise by premise.

(1) This says two things: (a) that for every p there is a q such that p entails q; and (b) that it is impossible to derive a false proposition from a true one.  (b) is a necessary truth and goes without saying. (a) is probably true, but it won't give Mr. Vincente his chain of truths.  It is equally as possible that the totality of truths interlock in a non-patterned way rather than "going somewhere" so to speak.

(2) This says three things: (a) there are an infinite number of true propositions; (b) these are arranged in a chain/hierarchy; (c) the end(?) of this chain is God.  The important thing here is that none of (2a),(2b) or (2c) follow from (1).  (2c) is highly ambiguous.  If God is the totality of true propositions, nothing has been proved beyond the fact that there is a set of true statements.  If God is more traditionally theistic in nature, then the argument simply fails to prove anything at all.

(3)  This follows from (2) unproblematically.

(4) and (5)  The only way this can work is if we rephrase "God does not exist" as "There is no totality of true propositions", which is a contradiction that proves its opposite and is non-controversial, but to say that as soon as we have a true proposition we must admit theism, is not tenable.

Rather than an argument for theism, Vincente seems to be more stating a belief in something similar to Transcendental Idealism.  Broadly, I think Vincente and those who hold similar positions, fall into the same error.  We must see the world primarily as a collection of things, not propositions (this is the respect in which Wittgenstein takes his system one step too far in the Tractatus).  Propositions must always point to things, otherwise they are purely formal.  God is Truth not in Hegel's or Schelling's sense, but rather in Plato's.  God is Truth because He is the source of Being.