I agree Brady is a big part of the success they have, but there is more to it. I was watching how helpless the defense was because of the presnap shifts. Usually the QB will send guys in motion and then wait for them to get set before starting the audible. With the system they are running, they simply are not using an audible. The very second that the guys in motion set, the ball is coming out, leaving the defense with no chance whatsoever to read the offense. This is why they had the mighty Bills defense backpedaling the whole game.
The good news is Buffalo is doing a lot of the same types of presnap movement to throw defenses off. It's showing immediate results too. In fact some of the things NE does, they borrowed from Greg Roman's SF offenses. Buffalo has a lot more talent but they are just learning. It's going to be interesting to see how it plays out later in the season to see if Buffalo can catch up.