If you want to simplify how AlphaGo/LZ works, it's kinda like this :Has LZ also built up a model of the game for itself? Has AlphaGo? I'm confused as to the AI aspect. I understand how it uses MTCS and NN to solve the computation problem, but there's no AI in there, is it?
There is the intuitive part of LZ brain : the neural network. LZ see a position, and her intuition (the neural network) give her a list of candidate moves and a feeling of who's ahead.
And there is the reading process : the Monte Carlo search (even if it's not really Monte Carlo anymore, because there is no rollouts). LZ read the most promising moves, and use her intuition to evaluate the position
Her intuition (the neural network) is trained by feeding her millions of self-play games by previous versions of herself, she's told the result of these positions, and her intuition learn what's good (= what's work), and what's bad (what doesn't). And that's how her intuition get better over time.
Now, what's inside the neural network is quite mysterious, but that's not specific to go. It's a "problem" with all deep neural networks. You can train a network to tell if there's a dog in the picture with really high accuracy, but how exactly the neural network recognise the dog is not well understood.