The walls 50-100' away from your character are the focus of your attention, and when you whip your mouse around those walls and characters at that distance cover a lot of screen space in a very short period of time. In order to keep that movement smooth, the screen needs to be updated as often as possible. Most of these games feature melee combat and jumping or climbing obstacles. Your eyes stay focused on the middle of the screen where your character is, and the ground and objects at that range don't move across much of the screen, even when you change your view quickly. 20 FPS in Quake would have more chop than a Bruce Lee movie.
Racing games are often the most deceptive.
The nature of a race game is such that your eyes are often focused on a small fixed part of the screen that shows the road ahead, and the scenery scrolls by in a very regular fashion. Most racing games appear quite smooth even at mediocre frame rates. To do well at a race game, you need instant and precise control and feedback, though. If you're having trouble with a race game, turn down some detail levels to improve your frame rate. The game might not appear smoother, but you'll notice quite an improvement in the overall feel and response after a short while.