I don't personally include board gamers in the term "gamer" (not to say that's wrong) and retro-gamer to me means pre-HD consoles games or game types. So you can retro game using emulators on the Wii or iPhone or whatever. I actually call board games old-school games. Like "Let's play Old-School Risk!"
People that play those casino games, I'm not sure, I don't know anyone who does that, I'm sure they have their own scene.
I play pretty much everything and anything that's good, I'm not picky about genre and I have a 360/PS3 at work so I often play through my lunch hour or in any spare moments.
I got a 25 kill streak in COD:MW2 yesterday; Fallout 3, Wipeout HD, Drake's Uncharted 2, Little Big Planet, Bayonetta, Persona 4 (PS2) are all featuring heavily in my rotation at the moment, as is GOW1&2 HD re-release (in preparation for GOW3) and Forza 3
I have Gran Turismo 5 (delayed -AGAIN!), GOW3, Final Fantasy XIII and Heavy Rain (*faints*) all on pre-order (oooh good year for PS3!)
I've also been in the beta for Star Trek Online, it's okay. I don't think MMOs are for me.