Specifically for first-/third-person games this means getting the right sensitivity and disabling mouse-acceleration (or setting it in a very specific way for some hardcore quake pros supposedly).
Last time I checked, disabling mouse accelleration is a huge hassle and no working UI exists. The average gamer will not go into config files of the OS to try and find the right formula that makes their mouse move the way they expect it to.
This isn't really an important issue in normal desktop usage or point-and-click games. Thus support by linux developers is understandably lacking.