I think you have a valid point here, but it does not do anything to save this paper.
The paper claims to have refuted the possibility of what Searle calls Strong AI, but speculating that the universe has behaviors not describable with computable functions does not justify that conclusion. As Simonh pointed out above [1], Strong AI does not imply or depend on everything about the universe being computable, and even if it did, mere speculation that some unknown thing about the universe might not be computable would not justify inferring that therefore Strong AI must be impossible.
This paper is combination of an unargued-for tacit premise with a rather blatant case of burden shifting.