Go ranks are in "stones" that one player can give another as a handicap - except at the professional level where there's more relative equality of play and the stone-ranks are honorary and ELO ratings are more accurate.
Monte Carlo tree search had advanced computer Go from 2-3K to 6-7 dan, a gain of 8 stones. Alpha Go apparently has advanced to 9-10 stones, professional level, by using neural networks to enhance the final position and search policy used in Monte Carlo tree search.
In many ways, it seems to me that Monte Carlo Tree Search was the primary answer to how computers could deal with Go [1].
Chess essentially conquered through a combination of red-black and other smart pruning algorithms, incremental advances in hand-tuned final position policy and improved hardware [2].
So it seems like the "conquest" of Go has involved a more generalized, self-learned version of the original approach to chess (tree-search strategies plus final position heuristics). That might enough for just about any deterministic game one can find.
It should be noted that Arimaa, a game designed specifically to be hard for computers without having the large board of Go, was "conquered" last year but without any neural net techniques (apparently).
[1]https://en.wikipedia.org/wiki/Computer_Go
[2]https://en.wikipedia.org/wiki/Computer_chess
[3]https://en.wikipedia.org/wiki/Computer_Arimaa#Techniques_use...