A gamer does not need to switch from the mouse to the keyboard repeatedly. Plus, a gamer cares about precision, which obviously a trackpad lacks.

"Faster" standalone means nothing. Can you move the pointer faster with a mouse? Of course. But I don't see most people flicking on their workstation.

In the context of this thread, "faster" refers to completing your tasks faster. And for that a trackpad beats a mouse if your job requires you to type a lot.

The point of trackpads (and even more so of trackpoints) is that they're faster to get to from typing position - you move your hand back a bit (or even just the index finger) instead of moving across the whole keyboard. That's not something that would go high on the checklist when gaming - it's usually one hand planted on WASD, the other on the mouse and hardly any going back and forth.