Just a half minute skim shows the author claims it passes the natural proof barrier but makes no claim about it being non-relativizing or non-algebraizing.
This is important because the Baker-Gill-Solovay theorem already demonstrates that there exist oracles A != B relative to which P^A = NP^A, but P^B != NP^B. This shows that the problem has contradictory relativizations, and hence can't be proven that way. This matters because it's a litmus test against quack proofs.
I don't think this is a problem here; the proof doesn't appear to be doing that.