I'm sorry but 10 day review time from this journal? And it's very much not a math journal.
At best, this is an argument that if our universe does non-computable things, then we can't be in a classical simulation. But if our universe does non-computable things, then CHURCH TURING IS WRONG, and we can build more powerful computers (or there should be some serious experimental barrier, which I do not see here), so we are again plausibly in a simulation.
In short, I don't buy this at all. Headline is literally false.