I would certainly consider musical genius to be a valid sub-category. Mozart, Bach, Beethoven, Brahms, Stevie Wonder, Elmer Bernstein, Henry Mancini, John Williams... I'm sure I could come up with others after some further thought.
I would acknowledge the possibility of literary genius and visual art genius, though I don't claim as much knowledge in those categories. However, if a person can produce a lot of really good work quickly and/or frequently, then that should qualify or at least point towards genius. In the literary world I would have say that Isaac Asimov probably would have qualified. He turned out a tremendous number of works, most of which were really good. I don't count the formulaic writers at all and there are a few famous and prolific writers whose work does nothing for me. For example, Michael Crichton seems to depend heavily on a semi-formulaic solution of Deus Ex Machina as the resolution to his stories. At least three or four of his stories that became movies ended in a disappointing way.
I tend to have a strict definition of "genius" so I have some trouble with "sports genius" tags where you are dealing with raw physical ability. I would not downplay the presence of the ability but just wouldn't tag it as "genius."
However, (try not to laugh too loud) there is the issue of golf. There are a lot of folks who can "grip it and rip it" and make impressive shots (John Daly and Bubba Watson for two), but it is the delicate or unusual shots that stand out. Tiger Woods sees shots that nobody else seems to see, and he all too frequently makes those shots. Granted, his body has been giving him fits with back problems and that has interefered with his career, but he has become a significant contender again now that his surgeries are over and his rehab has him in a good place.