Has any commenter here read the blog post? He starts from "network that evolves through simple rules" then goes on to derive how this results in space dimensionality, time, Sr, GR, the uncertainty principle, path integral, entanglement, and makes predictions along the way.

This is regardless of the specific rule that computes our universe. Also since that rule is Turing complete, it's going to be the same as every other Turing complete rule, and since we can't produce a machine IN the universe that can simulate the universe, it kinda doesn't matter what the rule is.