They made simple categorical error in the paper.
Computable systems can have have mathematically undecidable problems inside them.
Game of life is maybe the simplest example of simulated universe that contains many undecidable problems.
They fall into the same categorical mistake as the Lucas–Penrose argument, and they even use that argument in the paper. There is a lot of hand-waving. By the way, just adding irreducible randomness into a computational system would make it trivially non-computable in the meaning they use, but that itself would not prevent developing an axiomatic Theory of Everything that explains everything we want to know. So far, there has been nothing that demonstrates that the Universe must be non-computable.