So far, studies I‘ve seen mentioned in newspapers making a claim either for or against a correlation between chess and intelligence strike me as highly dubious in their methodology. That‘s not surprising, since the concept of a “general intelligence” is itself dubious. (And it’s not even entirely clear in every context what “intelligence” actually means.)
Chess is basically a duel that two people fight with their minds. One would expect that as a pastime it’s more attractive to people who enjoy exercising their minds in various areas in general. Therefore, it wouldn’t be surprising to find that among good chess players there would also be more people than average that are good at mathematics, spatial visualisation, music and arts, programming etc.
(Speaking metaphorically: A rooster makes cock-a-doodle-doo, because the sun goes up. It's not the other way around: The sun doesn't rise because of the rooster.)
Developing, for instance, a good memory for chess games and long variations doesn’t automatically grant a good memory for reciting poetry or repeating the dance steps in a choreography or the memory necessary to keep one’s focus through deciphering a particularly difficult classical Greek text. Nor does it make you good at drawing portraits (which is for a very substantial part about having a good short term visual memory).
There might be some soft form of synenergy in that playing chess increases brain activity, brain metabolism etc. which conceivably might have a positive effect on other mental activities. That, though, would also go the other way around.