But the game's rules are simple, the total storage of state needed for a game is rather small, so in terms of utilizing training data it's quite easy. You can fit an entire Go game in like 2 kilobytes of memory. There's only two types of stones, and they have no meaning other than being different than each other.
We would need more breakthroughs for real-time games. Compared to Go, they have easily gigabytes of potentially meaningful data PER game. Not only is storing millions and millions of games becoming an issue, processing them is becoming an issue as well. And in many of those games when strategy changes depending on which character or map you're on, it quickly balloons out in a manner that is just not reasonable.
Maybe the next step will be specialized AIs that tackle small more easily calculable components of real-time games and then combining those together to make something decent.