Here is one thing I don't understand about these kind of approaches. Doesn't a computational simulation imply that time is discrete? If so, doesn't this have consequences for our currently best physical theories? I understand that the discreteness of time would be far below what can be measured right now but AFAIK it would still makes a difference for physical theories whether time is discrete or not. Or am I mistaken about that? There are similar concerns about space.
By the way, on a related note, I once stumbled across a paper that argued that if real numbers where physically realizable in some finite space, then that would violate the laws of thermodynamics. It sounded convincing but I also lacked the physical knowledge to evaluate that thesis.
Time and space aren't well defined, but current models indeed put a discrete limit on both: Planck-Length and Planck-Time (~1.9×10^−43s and ~5.7×10^−35m respectively).
Below these limits, physical descriptions of the world lose meaning, i.e. shorter time spans or distances don't result in measurable changes and our models break down. That doesn't mean these limits are "real" in the sense that space and time are indeed quantised, but experiments and observations end at these limits.