This is what happened to quite a few people with the Toyota unintended acceleration issue. There was speculation that it was caused by bugs in the engine control unit. Officially the cause was found to be floor mats coming loose and holding the accelerator down. (I bought a new Toyota shortly after this and the dealer was very careful to show me how the floor mats worked and how to make sure they were properly attached.)

The brakes of a car in good working order should be able to overcome the engine and stop the car even if the engine is stuck at full power. But you have to do it decisively. Push the brake pedal to the floor and keep it there until you've stopped. What often happens is people are (very naturally) confused and not sure what to do, they'll brake but not hard enough, stop braking when it doesn't seem to work, try again, etc. This can heat up the brakes to the point where they're no longer effective enough to stop the car, and then you're really in for it.

I was with a friend in a 5L V8 Mercedes, and we were doing a quick drive around the block after some sort of maintenance. He floored the accelerator - I can't remember why that was required, except I assume it wasn't. I assumed he was only going to do it momentarily, but the car rapidly reached, and passed, stupid speeds for that road. Just as I started to say something about preserving lives of us, and anyone else on the road, he suddenly shifted to neutral and brought the car to a stop with the engine screaming away at the redline. He then calmly reached down, unjammed the accelerator, and then continued driving back home.

That car was automatic, but he drove cars with manual transmissions a lot, so that would make it an obvious thing to do. I think in some of the famous unintended acceleration crashes, it has been unclear whether the person tried to change to neutral. A lot of newer cars have a much less intuitive method of doing so as well.

There's nothing as good in this regard as cars with manual transmissions though, in terms of having a dedicated pedal which disconnects the engine from the wheels, which you practice constantly during daily use.

Seems like he wasn't able to get it out of gear, and then didn't want to turn off the engine because he'd lose power steering. Losing power steering isn't ideal, but seems like it'd be better than traveling at 135 mph, power steering is most important at low speeds, and I'd think better to have a bit of trouble with the steering as you get it stopped than to end up crashing it.