In conclusion, it seems, chess is technically on-topic but typically not asked. My question is from a slightly different angle: if there's a SE for it, why is it on-topic at all? Should all posts tagged chess be closed or migrated?
It has always been the philosophy of the StackExchange network that determining whether a topic is on topic should be done on a purely per-site basis, without considering whether the topic is on topic on any other site. This means that it is OK if some questions are allowed on multiple sites, and it is also OK if some questions are not allowed on any site.
There's alot of overlap between different sites on Stack Exchange, Stack Overflow for instance overlaps with Code Review and Database Administrator, and to a lesser extent Server Fault, probably more but those are the ones where I am a member.
While there are many other sites that could carry some questions, so long as they meet the intent of the site they are posted on, they are on topic. Chess is a board game, so it fits the Board & Card Games exchange site. We may want to mention to those posting topics for games that have their own exchange that the other exists, in case they don't know, more specific sites are likely to get better quality and quicker answers, due to everyone there being interested in the more specific topic, and no questions from other topics pushing their question down the page, but that doesn't mean we should move the question.