For instance, as any protoss player knows this all too well, a Zealot placed a mere pixel away from where it should could allow a stream of zerglings in, completely throwing any game plan you had up to that point out the window and enter crisis management mode. Usually this is a "mistake", which a computer may never make, but it needs to learn the relevance of such pixel-sized mistakes, which is unlikely to have as much of an impact in a poker game or Go game as it would in StarCraft.
I agree with your point, but you need to look no further than the game that AlphaGo lost against Lee Sedol.
It committed a very bizarre mistake that made no sense gamewise.
I think that there are two distinct aspects of the incomplete information that are significant; first, ignoring temporality, you have the fog of war, so you can't see the whole board. This is probably easier to address in a RNN, since you can play quite well as an amnesiac that just reacts to things that are currently visible. But you need to scout less if you have a memory of what's out there, so the amnesiac won't be able to play optimally.
Then there's the temporal aspect. The set of previous states of the game is not stored in the game and made available to the player, and so to play optimally you have to have a memory. This is where new techniques will be necessary.
These are separate problems, I think, so it will be interesting to see if DeepMind can make progress without reaching human performance on the second part.
There's already been excellent progress in poker AI based on traditional game theory, see http://poker.cs.ualberta.ca/.