I don't think they refer to Bayesian probability as probability. The abstract is ill-defined (according to LessWrong's operational definitions), but their point about ontological probabilities originating in quantum mechanics remains. It, I think, remains intertwined with multiverse theories, as multiverse theories seem to explain probability in a very similar sense, but not in as many words or with such great claims.

Also, in a classical simulation, I would not see probability working as it should to be obvious at all. In fact, it's quite difficult to imagine an actually classical system that also contains randomness. It could be that the childhood explanations of physical systems in classical terms while seeing randomness as present is clouding the issue.

Whichever way. I don't think it's really worth much argument. Just as a basis in probability theory.