Actually, I now strongly suspect that many (though certainly not all) of the claimed benefits of exercise originated from the same error as seen here. But that is a claim that would require substantial research, to separate the real benefits from the fake ones and get the true effect sizes.
Frequent dancing causes a 76% reduction in the risk of dementia. The benefit seems to be from freestyle social dancing, though I don't think that part is as well-verified. The benefit seems to be from making large numbers of quick decisions.
I wonder if playing jazz has similar good effects.
For something a little geekier, Shiva Nata, a system of keeping the mind fresh by doing more and more complex movements. The author of the blog is a silly person, but the system seems to be for real.
Edited to correct html which was entered in the text field instead of the html field. It wouldn't surprise me if having to deal with electronics and computers tends to prevent dementia, considering the number of fiddly and changing details one has to deal with. Or is fun required?