Modern commercial board games and some genres of video game have communities that could continue for a similar length of time, but they’re still too young to have reached a consensus on one or two games; I suspect that’s a few decades out. The good news is that there are some older titles that are still holding their own in the market— to beat out the newcomers hints that there’s some kind of staying power there.
Two of the more well known variations are shōgi and xiangqi: Shōgi allows the redeployment of captured pieces, whilst xiangqi limits the movement of a few pieces and has a mechanism for representing artillery. I find that each game has a very different character to that of western chess, even despite the fact that they share a large number of tactical motifs.
Western chess may be the most popular variant world-wide, but that's no indication that it is at any kind of pinnacle.
Basically, train really strong AI players using the AlphaZero method with the rules of the game changed by a human author (either some variant of Go, or a completely new game). Then take a look at the games the AI plays at its strongest level and let people decide if the game looks interesting enough for them to try play competitively. With the strong AI player already in place, human players would have something to learn from and a serious competitive culture could be born.
In the absence of something like this, I don't think it's surprising the only popular ASGs are very, very old. Modern commercial board games are fine, but they supply a different demand than ASGs.