Probably, but probably not publicly.
What you're asking for here is a very valuable bit of marketing data. I have no doubt that such a survey has been done, either by a big tabletop gaming company like WotC, or an independent marketing firm hoping to sell such data to other tabletop gaming companies. Putting together a study that shows the shape of the tabletop RPG hobby with any semblance of accuracy is going to be a difficult - and thus expensive - prospect.
In order to accurately know who is playing what games, there are a number of non-trivial factors to account for. For example, it's non-obvious where the lines are between different genres in the hobby. There are a large number of games that straddle lines between popular genres, and figuring out useful data out of player numbers for that kind of information is difficult. In addition, there's the problem of players who play more than one game. Do you count them under the game they play most? Do you count them under all the games that they play? I've personally played a few sessions of World of Heroes and Tyrants back in high school, does that mean that I should be counted in the W.H.A.T. bucket? What about mods and houserules? If I run a modern setting heist game using the Dungeon World ruleset, what genre of game am I playing? These kind of questions are the things that marketing analysts get paid to answer.
Thus, I'd be willing to bet that, while such a study probably exists, it's not available to the general public, and would be prohibitively expensive if it were.
