I think what might end the popularity of standard chess worldwide some day would be a high rate of draws in top level chess, and opening theory regarding the best openings becoming exhausted (the Black side in particular finding it ever harder to get a fair rate of wins in high level chess). I'd note that poor 8x8 checkers still seems to be going in terms of some popularity, and has events with cash prizes, in spite of any trouble with draws at the top level, or exhausted opening theory (one section of two in world championship checkers starts with a sequence of 3 randomly chosen moves). Checkers may last at least several decades more, so I'd guess chess' popularity won't dramatically drop for a century or more.

I used to think computers being better at chess would dramatically drive down its popularity in time, but this doesn't seem to have happened. The danger of computer-assisted cheating is something people grapple with in a number of walks of life, as a consolation, and lots of people seem to think it's no different for machines to outdo people in racing, so why not in mindsports? In any case, games that feature (or add) elements of chance such as cards don't seem more hopeful in this regard, as e.g. Poker is now being very well played by computers.

I've thought that as long as standard chess dominates, for whatever reason, one or more chess variants (other than regionally popular ones) won't have much of a hope of coming close in terms popularity, i.e. to share the stage with chess (at least over-the-board), much as there is more than one Poker variant played at Poker events. On one chess server I've noticed only about 2% of all games played are chess variants, half of which are bughouse, and much of the rest being crazyhouse. So, I see no next chess making much headway for at least a century. However, let's assume I'm wrong about that, but not about high draw rate in high level chess and/or exhaustive opening theory killing chess off. The next chess would have to fix those serious problems, and any others, without being too repulsive in some way. Chess960 may not solve the problem of high level draws, and some random setups favour White or may even make for a more drawish game. Shuffling the pieces at setup time may be a useful idea to keep in mind to stop exhaustive opening theory, if suitable for a given variant, however. Another way would be to use cards to randomize openings further, at least, though there's always some element of chance then, which a chess purist may dislike.

I invented Sac Chess (10x10), which has 30 pieces per side, as an attempt to avoid high draw rate, and allow for virtually inexhaustible opening theory, though as always extensive play is needed to be sure. The game also may allow for shuffled pieces in the setup as a variant, with some sort of castling rules being added, as a way to further make theory inexhaustible. However, again extensive testing would be needed to see if all shuffled setup positions would be fairly playable, i.e. more than for Chess960. Fwiw, I had initially hoped Sac Chess might be computer-resistant to some extent, but I've become pessimistic about such a hope for any game, should computers and programming continue unabated in terms of progress. In any event, Sac Chess has not been much played yet on Game Courier.

I've looked a bit at some other 10x10 games, and to my surprise not many seemed to be inexhaustible in terms of future opening theory. Such a large board, plus more than 20 pieces per side, may be best, to hope for inexhaustible opening theory (Knightmare Chess is 8x8, and with the help of its card decks it may not have a problem this way). 12x12 Gross Chess has a lot of pieces, and they are not mostly very powerful (as is the case for Sac Chess, if that's a drawback). I don't have an idea of whether Gross Chess takes a large number of moves on average to finish a game (chess has a nice average of 40), but the game is already popular on Game Courier, at least. For a coffeetable I can picture 10x10 being nice for a decorative set in some possible future reality, but I'm not such if 12x12 would be too big. For comparison, the board game of Scrabble is 15x15, albeit with small cells and tiles. Such are some factors to consider when hoping a variant might prove to be the next chess some day.