> With inputs and outputs, one could conceptually write and run any software in it.

IO is major caveat though. And there is also real-time to consider.

I've been long wondering if we should define more interesting computer models in addition to Turing machines. Games make interesting milestones as an example; you could define a system to be e.g. "Tetris-complete" if you could run a playable version of tetris on it, or more advanced would be "Doom-complete" and simpler could be "Chess-complete" or "Zork-complete". Each model would imply something about not just pure computation, but the practical capabilities in terms of inputs and outputs and also something about performance. Of course it doesn't need to be games, you could use anything as a basis for a model.