> How do they try to stop it now?
Generally, they don't. They have an in game reporting function, but it doesn't seem to do much good. Many cheaters live stream their exploits, seeing people through walls, getting 100%-accuracy-all-head-shots, etc. The net code that's responsible for reporting where you are aiming is separate from the data/code that reports where your bullets are sent, so some cheaters show off by shoot directly at the ground below their feet while magically killing people several hundred feet up above in a helicopter.
The experience is often pretty bad, and yet people still play the game...
Yes, it makes competitive/casual play crap. In CoD in particular, it is out of control.
> How do they try to stop it now?
A variety of ways, ranging from server-side analytics, player-driven report systems, manual review, the game inspecting its own state, processes that spy on your computer, and rootkits. Each and every one of these has different advantages and drawbacks.
> Do they really need a kernel driver?
Given how ineffective anti-cheat efforts in CoD have been, it's possible that they need a kernel driver to bring it under control. It's possible that a more talented team would not.
It's when there's a whole cottage industry around this that you know things are out of hand.