I looked at your website, and from my experience I'd say that it's Facebook's mistake,
In the message you got, did it had a button that says "file for an Appeal"? if so , click that and explain that it's one of the games that can be used with your gamepad, it's not a game that you're promoting and your not suggesting people to play it, as what might have happens is that the auto engine listed the photo of the guy holding a double barrel shotgun as a violent image, or as an image against the weapon policy (two different sections):
I don't see any other reason why your website is not approved for advertising,
I believe that they'll allow it if you appeal, and you may also get a better explanation from them,
If not, the best next step will probably be to remove the guns and shooting scenes from your website and choose other games to promote.