I don't consider myself a hardcore gamer (I rarely play online, for start), but I do like to occasionally play 4x games (Civ 5 and many space 4x games like Endless Space or Sins of a Solar Empire), flight simulators and generally simulators of something (SimCity etc.)
I have this wonderful rig in my studio with three large monitors and a pretty beefy GPU and I've got to use it for something other than just music software...
I've never written game music and generally I find it the most cliched of any type of soundtrack. With the usual rare exceptions, of course.
Desktop: i7 3770k, 32 GB RAM, nVidia GTX770 + GT640-DCSL fanless, 3 monitors (30" 2560x1600 + 2x 27" 1920x1080), 256 GB SSD (OS), 2 TB SATA III (audio), 3 TB SATA III (sample libraries), 3x 3 TB USB 3.0 (backup/archives), RME UFX, Win 8.1 Pro x64, Cubase 7.5, Sonar X3, Vienna Ensemble Pro 5.
Slaves: 2x i7 2700k, 16 GB RAM, 256 GB SSD, 3 TB SATA III, Win 8.1 Pro x64, Vienna Ensemble Pro 5.
Laptop: 17" HP EliteBook 8770w (i7 3820QM 2.7 Ghz/3.7 Ghz max OC, 16 GB RAM, 256 GB SSD, 1 TB SATA III), RME Babyface, Win 7 Pro x64, Vienna Ensemble Pro 5, Cubase 7.5, Sonar X3.