In particular, computers are nowhere close to beating top humans despite the fact that there has arguably been even more effort to make good computer players than good human players.

Reportedly this just happened recently: http://games.slashdot.org/story/15/04/19/2332209/computer-beats-humans-at-arimaa

Arimaa's branching factor dwarfs that of Go (which in turn beats every other commonly known example).

Go is super close to being beaten, and AIs do very well against all but the best humans.