My dad has played games like FPS and TPS, but very infrequently nowadays. He occasionally has a go at whichever Grand Theft Auto game someone else is playing, and usually gets into police chases.
My mother, on the other hand, plays games regularly on the PC. She likes racing games and third person action adventure games (ranging from the earlier Tomb Raiders to Mafia and Grand Theft Auto: San Andreas) most of all, and often plays some classics on the Amiga emulator (like Lemmings!) but she also plays -- get this -- Operation Flashpoint. The first one. The open-world, tactical FPS military simulator from 2001.
I forced her to try it years ago so she could play the cooperative missions with my sister and I, and it's the first FPS she's played since she played Wolfenstein 3D and Rise of the Triad in the early 90s. To my surprise she came to really like it and has been playing it in her own time. She's not as adept at the more in-depth aspects (like squad AI control and commanding tanks) as I am, but she's a capable infantry soldier and particularly loves sniping. I think she enjoys it more than conventional first person shooters because it's slower paced and succeeding in it relies more on patience, tactics and a steady hand than on fast reflexes.
I'm currently trying to get her to try STALKER.