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This year top human Arimaa players (including 2 world champs) were beaten
by a computer program, seemingly ending the hopes of that game of remaining even remotely computer resistant. That is, unless humans come up with fresh strategies for the game, but I suppose it is no longer as easy to do that since Arimaa is not such a novel game anymore. 

Based on what I've seen on the web, Arimaa had many attributes that at
least one of its champions thought might make it computer resistant. IMHO
it lacked being played on a board significantly larger than 8x8, which
might have helped since in the case of Go, so far it seems clearly the
larger the board size, the better. 

In Go, I would note that the number of legal moves is not excessively
large, even in the opening phase. Go has the advantage over chess that
there is no king or more than one type of piece, making it tougher for a
computer to evaluate a given position. I've also read that a good Go player can at times easily assess how important a single stone might be for 100 ply ahead, by contrast. This helps with both evaluation and pruning any search tree of moves not worth looking at very deeply.

My own guess is that for chesslike games board size could be important, and having a larger number of moves available on average than in chess could help too. Having Shogi-like drops would help greatly increase the average number of moves, and such can be visualized more easily in a way IMHO than some complex long range [fairy]chess piece movements. 

A problem with drops is that computers can visualize checkmating sequences
of moves better than humans, but this problem would vanish if a player can
drop a piece only on his own half of the board, assuming a variant that is
similar to Shogi. Shogi programs at the moment are close to top human skill level afaik, but a larger board variant and a suitably modified drop rule (if necessary) might make for one type of variant that may be computer resistant for some years to come, I would guess.

All this assumes that alpha beta or some sort of tree searching with modern computers would be
used, but there could be fresh danger for humans when vs. engines if neural net programming becomes sufficently advanced, or practical quantum
computers become available, especially to the general public.

A while ago I saw a variant on this website that was a cross between chess
and Go, in that some sort of checkmate was possible, and there were example games that
lasted a reasonably short number of moves, like for standard chess. If
someone can find it (whether or not before me), perhaps it can be assessed
as to whether it might possibly be just one chesslike variant that is computer resistant. Meanwhile, I had
some faint hope that some of my invented variants (or anyone else's) might
prove computer resistant, if any ever become popular enough to attract the
attention of serious programmers. All my invented variants to date are now
listed on this website fwiw.

edit: The game I'm thinking of is Gess, where in fact no checkmate ever occurs. Thus, not what I had in mind to be a chesslike game, but it still looks interesting otherwise:

http://www.chessvariants.com/crossover.dir/gess.html