What would be a good starting point to learn about the AI behind that for a "normal" programmer? There seem to be so many resources now that it's hard to choose. Combination of hands-on plus theory would be good.
From there, Coursera has a paid(?) DL course by Andrew NG or there's Fast.ai which looks good.
Good luck!
http://shop.oreilly.com/product/0636920052289.do
For reinforcement learning, I hear Barto and Sutton is very readable, but I haven't read it myself. You can just pick the concepts up by reading papers. The introduction in the Deep Q-Learning paper is not great, but it's how I first learned the concept.
http://ufal.mff.cuni.cz/~straka/courses/npfl114/2016/sutton-... https://www.cs.toronto.edu/~vmnih/docs/dqn.pdf
By the way, I believe David Silver was the lead programmer for AlphaZero.