When the AI is cognizant of the fact that Go is a game, and knows what a game is, and perceives that the game is taking place in a larger reality, where there are other things happening while the game is going on....then I'll be impressed.
You can make some analogies between sparse matrix data representations and what happens in the mammalian neocortex. It is of course not self conscious, but it effectively deals with semantic information and relationships among it.
Or maybe not. The history of AI is one of humans always moving the goalposts when AI advances.
Chess? just a computationally simple game. Driving? Well it's just physics. Go? now that requires intelligence oh wait, just some deep neural savant thing, not real AI
The sheer amount of computing power that AlphaGo needs will be a problem for games as complicated as Go for people who aren't Google. There will probably be more activity in simpler games with interesting properties.
Non-game applications will require a fully formalized set of rules. The fact that formalizing what you want is hard is the reason we need programmers in the first place, so nothing fundamentally different there.
I did some work for a Forex trader. He had devised an algorithm for trading and used it daily for modest gains. He engaged me to automate it for him via the vWorker freelance website [1]. I got the engine going getting the realtime price data etc. But when it came to his system it didn't work. In practice he didn't always act upon the signals he thought he did. We ended up in payment dispute because he insisted that if I had done the work right then the bot would be making money. By this time, I had learned the error of his thinking. We arbitrated on 50% payment - I wasn't too pleased with that but I had learned about trading.
I do feel that given all the hype and speculation about strong AI researchers in Deep Learning should really come forward to contextualize the real impact of this - which I think is not all that great.
You can expect a lot of advancement in actual games very soon, including ones with randomness, and after a few years probably hidden information games too. Being able to specify real-world problems as formally as a board game is now a more effective skill than it was before (it was good already).
It is also good enough to put it in a combat drone that visually recognizes objectives and people. This can be all commanded by a small group of people, anonymously, and detached from accountability and without casualties.
To say nothing of the casualties that'll be inflected on the AI warriors...