Plenty of people make fanart, doujins, and the like, which is probably more analogous to what most people that play instruments and make music do.
Speaking of this, I've always thought it was strange that I love anime and manga just as much as music, but have never had the desire to do anything related to it other than watch/read it. But with music, I've always felt the need to create it was well, and learn as much as I can about it. I don't really think of myself as a music otaku, though, because my interests and knowledge are pretty broad and generalized. And, pretty much everyone is into music to some degree.