I think this paper (while mathematically interesting!) is rather oversold. A positive result to their proposed experiment says one of the following is true:

A) we're simulated on a cubic grid B) we're not simulated, but True Physics has cubic structure C) (other non-obvious cause of anisotropy)

Not only is it very difficult in my mind to distinguish between A and B, think what a negative result means; one of:

A) we're simulated on a non-cubic grid B) we're simulated with a more complex discretization that deals with anisotropy C) we're not simulated, and True Physics doesn't have a cubic structure

I think the only thing a cubic anistropy can tell us about is the structure of True Physics, not whether or not that true physics is based on a simulation.

Thanks.