I don't think there is anything that requires super-fast response times either, so you could conceivably get ~1 frame per second and not lose much information.
Well, IIRC, there are some visual indicators that rely on blinking, but I don't think they are crucial.
A typical game might last 15 minutes = 54000 60fps frames and a typical map is larger than 10k x 10k in terms of 'coarse units'.
For any given frame of animation there are at least a million valid actions - if you have 10 units then you can move any subset of those units to any place on your screen.
That depends entirely on how you represent it. You're forgetting that there are plenty of AIs that actually play the game right now. They just don't use the same kind of "interface".
>For any given frame of animation there are at least a million valid actions
That's Google's marketing cool aid. "Actions" that produce the exact same result cannot be meaningfully counted as separate actions, especially when you're trying to compare them to board game moves.
Also, the dimensionality of the state space in a "continuous" game is orders of magnitude larger. In a game like chess or Go, you may have dozens or hundreds of moves available at each turn, but only a few of them will be "locally optimal". In StarCraft, there are many more degrees of freedom -- attack timing, positioning, formation, banking versus spending resources, and so on. A good AI will need to be able to abstract that huge state space down to something more tractable.