[gambler]

>Even with the restrictions you put in place, SC2's state space is much larger than any board game.

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.