Great example! Failure modes are really important. Brains and dwarf fortresses might both be computers, but their different physical instations give them different ways to break down. Sometimes that's not important, but sometimes it's very important indeed. Those are the sorts of things that get obscures by these dogmatic all-or-nothing arguments.

I'm just cautioning against taking things too far in the other direction: I genuinely don't think it's right to say "your brain isn't a computer," and I definitely think it's wrong to say that it doesn't process information. It's easy to slide from a critique of the computational theory of mind (either as it's presented academically by people like Pinker or popularly by Silicon Valley) into the opposite--but equally wrong--kind of position that brains are doing something wholly different. They're different in some respects, but there are also very significant similarities. We shouldn't lose sight of either, and it's important to be very careful when talking about this stuff.

Just as an example:

That is all well and good if we functioned as computers do, but McBeath and his colleagues gave a simpler account: to catch the ball, the player simply needs to keep moving in a way that keeps the ball in a constant visual relationship with respect to home plate and the surrounding scenery (technically, in a ‘linear optical trajectory’). This might sound complicated, but it is actually incredibly simple, and completely free of computations, representations and algorithms.

It strikes me as totally wrong to say that this process is free of computation. The computation that's going on here has interesting differences from what goes on in a ball-catching robot powered by a digital computer, but it is computation.