I didn't take Tegmark's argument to be a computational theory. I took it to be an inductive one based upon the trend of the physics over the last decades towards the more and more generified multiverse theories. Ultimately, you land on a model where all consistent mathematical representations of a reality exist. At that level of abstraction, there is no where to go: it is the limit of the induction. There's a rather satisfying sense of self-evidence about it, but that doesn't mean it's falsifiable or true.

IIRC there are no arguments about computation or what underlying medium(s) are involved, it seems like a separate question.