Almost any game that their AI can play against itself is probably going to work. Except stuff like Pictionary where it's really important how a human, specifically, is going to interpret something.
I know a little bit about training neural networks, and I think it would be plausible to train one on a corpus of well-played StarCraft games to give it an initial sense of what it's supposed to do, and then having achieved that, let it play against itself a million times. But I don't think there's any need to let it watch how humans play. If it plays enough games against itself, it will internalize a perfectly sufficient sense of "the metagame".
If we're talking about AI in RTS games, I've always dreamed of the day when I can "give orders" in an RTS and have the units carry the orders out in a relatively common-sense way instead of needing to be micromanaged down to the level of who they're individually shooting at.
So chess and Go are both games of perfect information. How important is it for the next game that DeepMind is trained on to be a game of perfect information?
How would the AI perform on generalized versions of both chess and Go? What about games like poker and Magic the Gathering?
How realistic do you think it's possible to train DeepMind on games of perfect information (full-map-reveal) against top-ranked players on games like Starcraft, AOE2, Civ, Sins of a Solar Empire, Command and Conquer, and Total War, for example? (in all possible map settings, including ones people don't frequently play at - e.g. start at "high resource" levels). How important is it for the AI to have a diverse set/library of user-created replays to test itself against, for example?
I'm also thinking... Shitty AI has always held back both RTS and TBS games.. Is it possible that we're only a few years away from non-shitty AI in all RTS and TBS games? Or is the AI in many of these games too hard-coded in to actually matter? (e.g. I know some people who develop AI for AOE2, and there are issues with AI behavior in the game being hard-coded in - e.g. villagers deleting the building they're building if you simply attack them).