Yes it does unless one’s being pedantic: A statement of precision beyond which t

Yes it does unless one’s being pedantic: A statement of precision beyond which the analogy is meant to inform.
Yes, the only rules governing the operation of the universe produce the equivalent of computation by trial and error within those rules. Computation need not be declarative and with intent, it can, conduct experimentation by trial and error.
Why? Because like computation, there are only so many operations available at every scale of complexity.
As such we do see as (+) Accumulation (supply), (-) Accumulation (demand), (=) Stabilization(Persistence), and (!=) Dissipation to Collapse.
Giving us states and operations (those combinations that persist). Which results in computation.
If you mean is there a program? Of course. Was it composed? No. Did it evolve? Yes, but by the same rule: survival.
The laws of the universe are those that could survive. We just haven’t quite understood what’s happening down there in the quantum background prior to the formation of proto particles and particles.