Now that this milestone has been reached, does that represent a significant advance in artificial intelligence techniques or was it just a matter of ever more processing power being applied to the problem?
Neither, really. It is a milestone and a significant advance in computers beating humans in games, but the techniques used are only relevant to that game, not for other purposes in AI.
The solution lies in humans analyzing the game and implementing algorithms for finding a good move. This is the main reason that a computer can beat the humans, together with the fact that it can calculate much faster and that it doesn't make really bad moves by not seeing something.
Processing power helps, but the game-tree complexity for Go is very large, estimated to be larger than 10200, whereas the game-tree complexity for chess is only 10120 (known as the Shannon number), so chess is less hard. This means that for neither chess nor go a database can be created with all possible positions.
The fact that Deep Blue beat Kasparov in a six-game match in 1997 was quite a development since this was one of the first "hard" games where a computer beat a top human. But it still isn't really Artificial Intelligence, more analyzing the game. Implementing an opening and endgame book was a large part, the middle game was done using analysis, I don't know the details.