Two approaches used by the previous version of AlphaGo (MCTS and a NN for position evaluation) have been tried in the past in computer chess with relatively poor results, while in the past few years they were already giving good results for Go.
The current version might be using some different techniques that could be more useful, though. They should release some details in the next few weeks.
Can't they effectively "solve" chess with the power of AlphaGo? Someone posted on the last thread that the AI plays one game of go every 2 seconds against itself to train (that's ~150 moves/second). Wouldn't chess be solved for all combinations in a matter of days?
Short answer is no. One estimate says there are 10^120th possible chess games. I'm not doing the math now, but I believe that falls into the not-physically possible within our lifetime using known physics.
An "If you had started calculating at the beginning of the universe, you wouldn't have even tackled a sliver of the work by now" type of problems.
What I mean by solving "every" move is that the AI would be able to determine which trees are a "losing" state and not continue, removing well over 99% (or 99.999% I don't know) of the possible games. I guess maybe solve is not the correct answer but something like 99% presumption on the best or best 3 moves.
AlphaGo's strength is in choosing which moves to consider. Solving a game means considering every move (up to alpha-beta pruning) -- AlphaGo's techniques don't help with this.
The current version might be using some different techniques that could be more useful, though. They should release some details in the next few weeks.