I read that too as soon as I saw thomblake's reply. I'm a newcomer here, and I hadn't heard of this view of physics before so it was very informative (though the quality of the wiki article isn't that high, citation wise). I've also been talking to a physicist/philosopher about this (he's been saying a lot of the same things you have) and he gave me the impression that if there's a consensus view in physics, it's that time is continuous...but that this is an open question.
Is this computationalist view of physics popular here, or rather, is it more popular here than in the academic physics community? It seems as though a computationalist view would on the face of it come into some conflict with the idea of continuous time, since between any state and any subsequent computed therefrom there would be an intermediate state containing different information than the first state. But I'm way out of my depth here.