Not “the exact same way”. You miss the point. Quantum mechanics is not some garnish on top of physics. It is all of physics (except gravity, so far, though nobody believes gravity isn’t quantum too). It explains how the sun works and how carbon atoms (all atoms in fact) cohere, how light behaves. Without it nothing works. But this argument treats quantum physics like some fringe thing revealing a flaw in the system. If the simulating universe is not based on quantum mechanics then it has no people, no computers and no atoms as we know them in it. And that contradicts all of the assumptions of the original premise.