I found Guitar Hero to be very skill based, not on natural ability. I'm not particularly great at most of the non-easy music games.
What I'm saying is that GH1 and 2, much like, say, Ouendan, fighting games, and Ninja Gaiden, were games where I noticed my ability significantly increasing the more I played, much more quickly than with other games.
So no, I don't think it's "natural" skill, it is acquired, or at least can be acquired, with sheer practice. You can't say that about all games, where frequent practice will definitely increase your ability, but you hit a wall pretty quickly after all mechanics click.