There are arguments which are wrong because they lack rigor, but in my opinion this isn't one of them. The main problem is asking a question about "actual existence" of abstract objects without clear understanding what such "actual existence" would represent. I can imagine a rigorous version of this post where "actual existence" was given a rigorous definition, but I doubt it would convince me about anything (as I remain unconvinced that e.g. modal logic is a useful epistemological tool although it can be formalised).

Note that (one of) the apparent motivation(s) of all recent anti-infinity posts is rejection of many-world interpretation of QM, i.e. it is unlikely that the author is aiming at constructing a neat rigorous theory.