Perhaps the simulation isn't time reversible, but that doesn't say anything about the reversibility of the laws of physics and the reversibility of the universe. I.e., reversing the entire universe would still run the simulation backwards, correctly, because it takes place at a lower level.

However, I think the point of the article is that given a deterministic universe, even though it doesn't "run" forwards or backwards but just exists throughout space-time, observers inside the universe can still observe an "arrow of time" in the direction of more stability.