I've been gaming since I was 2. If it looked fun, I played it. Hell, I nearly had a knack for it to the point of my siblings hiding the manuals from me to prevent me from playing them. Nope, didn't work. I figured them out intuitively anyway.
But yeah, I played games for the sake of playing games. No particular genre stood out for me. But if I must, it would have to be racing games. I always liked moving fast, and even optimizing my driving path. Gran Turismo (License tests) really helped me with optimizing my racing skills. Apply that to several other racers that can work similarly, and I can become a nightmare on the road/course fast. I just need a lap to familiarize myself with the track and car/character, and then you'll see me shave half a minute off my time easily; provided weapons are not allowed on track (unlike Speedrunners or Mario Kart). It's no surprise I can max-out a car's speed on a packed freeway in NFS or GTA, and dodge a majority of the other cars, and in some cases threading the needle at 200+mph.
Secondly, FPS and FP-Simulations (Flight/Mech/Space simulators; lotsa keys (immersion reasons), guns, and big things to blow up) games. Excellent stress relief/way to vent. Excellent way to learn ballistic physics while at it too. Flak and Biorifle Arena mode in Unreal gets hectic. Know your arcs, and time your shotgun blasts. However, nothing beats a Redeemer or BFG9000, and just how much big boom you get from them. Just as well, blowing up a Star Destroyer, or a base as big as a city, is quite satisfying.
Flying through the Death Star II, fuck yeah! The pilot proving grounds were fun too. Especially flying through a giant asteroid factory thing in an A-Wing at 250+MGLTs. In general combat skirmishes (Instant Action Mode), I always loved flying the
Cloakshape Fighter though; Like flying a deadly manta ray through space.
Honorable mention goes to puzzle and environmental games. Nice to relax to, or have a nice zen feel to it (like Antichamber, Lyne, Edge, Kairo, or Mirrormoon. Clickr is silly and difficult; Kami is a good counter-balance to that).