On your "divine command" bit: I don't think any theory has a good claim on the ultimate ontology of reality, so I don't see how one view is better than another. It's all some kind of divine command at the moment. Computationalism at least constrains the necessary properties the divine must have.
But that's just circular logic.
It begs the question as to what is "computational" and what is "mathematical". E.g. Tegmark has good points in the "Mathematical Universe" that describe possible interpretations of what it means to be mathematical. But how is computation different than math? I'd argue that computation is primarily stateful, logical, and (mostly) deterministic with a clear flow of time, whereas mathematical models are often time-reversible (as most, if not of QM is), stateless, and not necessarily "logical" in the sense of relating finite symbolic quantities. Rather mathematical models happily relate infinite series, manifolds, surfaces, high-dimensional spaces, they talk about fields and operate on functions, etc.
The universe must be inherently dynamical, ie., not mere discrete states that change by rules, but properties whose nature is to interact with the world...
This is why the abstract mathematical conception of "computer" cannot describe anything physical: mathematical objects do not have temporal properties; they do not change.
This leads to the illusion, for electric devices, that the change is extrinsic to the physics of the system since we can specify the algorithm (somewhat) abstractly. But it isnt.. your pieces of meat, are in the end, the causal power which moves the liquid crystal, electric field, etc.