where does AI go from here? Are there other high profile games to defeat, or has competition based AI run out of opponents?Not sure about "high profile" but there are a lot of other abstract strategy games out there, which might be candidates:
https://en.wikipedia.org/wiki/List_of_abstract_strategy_game...
But what a lot of people seem to be talking about is AI vs human in something like Starcraft. My personal hope is that researchers working on this kind of video game playing AI will use an Open Source game though, so it will be easier for others to follow along, participate, etc.
If you're Larry Page, what do you do with DeepMind now?
Good question, because it's hard to know exactly how well this generalizes to other domain(s). That would probably be one of the first questions I'd start looking into.