Fwiw, some world championship level players finally lost at Arimaa to a computer in a challenge match during 2015, as noted previously on CVP, i.e. that game has fallen, too.

Perhaps there can be no board game of skill worth playing that will forever not fall to computers. The progress of self-teaching algorithms & quantum computer development give me that sense, anyway. Finding enough memory for storing nodes during searches, to search deep enough for board games requiring such, might be the thing that's slowest to come as the years begin to go by, but I'm speculating, especially as a layman. The best hope for human board game players might even be if arguably less desirable technologies are somehow forgotten due to general divine intervention to, say, avert WWIII, but this is even wilder speculation. Fergus has suggested Knightmare Chess, which uses cards, might be computer resistant, but without playing I am less sure that this might not be so.

I recently reassured myself chess is still worth playing, in spite of especially computers. For example, they allow easier cheating, especially on the internet. However, chess is in good company, as technology has made cheating easier in other areas of life, such as in the field of education, and efforts are made to combat it. If chess is ever to be abandoned as dominant, the selection of a replacement game may depend on the reason why chess was abandoned. If it's due to opening theory being played out, only, then Chess960 would be a quite suitable replacement. Kasparov has suggested the same starting position be used for 10 years, then switched. I'd go farther and suggest 100+ years - it's taken that long for chess theory to be fleshed out as much as it has been to date. The reason I like a fixed start position is to help study & merchandising (opening books), which I think may have been a more positive than negative thing, say in the case of popularizing chess.