Most board game computer players use some sort of tree search followed by evaluation at the leaves of the tree. What we discovered in the 70s is that you don't need to have human-level evaluation to win at chess; it is enough to count material and piece activity, plus some heuristics (pawn structure, king safety...); computers more than compensate this weakness with their superhuman tree exploration.
This approach never worked so well for Go because evaluation was a mystery: which group is weak or strong? how much territory will their power yield? These are questions that professionals answer intuitively according to their experience. With so many parts of the board that depend on each other, we don't know how to solve the equation.
It looks like AlphaGo is the first one to get this evaluation right. At the end of the game, his groups are still alive and they control more territory. So Go evaluation is yet another task that used to be reserved to human experts and that computers now master. The fact that this is mixed with classical tree search does not make it less impressive.