I've played some FPS games with a trackpad for lack of having a mouse available, and on a larger, higher precision one (e.g., Macbook size) it was not a bad experience at all. You can move a finger a lot faster than a whole arm. Reflex high-res motion at the pro Counter-Strike level isn't likely, but for the casual gamer, trackpad FPS control absolutely seemed plausible. So I believe this kind of input will work for…
If you're moving your arm to move your mouse, there is probably something wrong with your mouse.