Most games aren't bottlenecked by your CPU at all. It spends a lot of time waiting for the GPU to be done drawing you a picture.
"Why isn't the game doing other stuff meanwhile?" you might ask, and part of the answer is surely, "Why do stuff faster than the player can see?", while another part is likely a need to syncronize the simulation and the rendering so it doesn't show you some half-finished state, and a third part might be that it would be very confusing for the player to decouple the game state from what they see on screen, like you see yourself aiming at the monster, but actually it moved in between frames so your shot will miss even if the crosshair is dead on.