That's what I get for running my mouth without looking at the paper. Skimming it now, the "dancing [was] associated with a reduced risk of dementia" result smells like multiple testing throwing up spurious crap. There's a dementia hazard ratio listed for 9 physical activities, and the ratio for dancing was the only one that was "significant" — but it's only barely significant as the confidence interval goes from 0.06 to 0.99! And the hazard ratios for the other physical activities are all over the place, half of them less than 1.00, half of them at least 1.00. There doesn't seem to be any real evidence of an association between exercise & dementia, taking this paper as a whole.
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?