What exaclty is allowing these guys to defy gravity?

Actually they aren't defying gravity. The stunt requires gravity to work. Assume the "bowl" they are driving in was in a stable Earth orbit. The bowl would attempt to rotate in some fashion to counter the drive force of the wheels. (That assumes they could get their engines to work ie they need oxygen to run the gas engines). With no "weight" there wouldn't be enough friction to allow an acceleration vector for the motorcyle/car's mass to develop.

To see the effect fail on Earth all you'd have to do is mount the "bowl" on a concentric bearing track with low resistance. Assuming that the engines could develop enough horsepower to run the wheels on a rotating surface, it would become fairly difficult to do the trick. The centrifugal force countering the wheel friction allows the cycles to remain "planted" on the bowl's wall. The angular momentum is keeping them circulating in the bowl.

Also you might note that as they slow down and "slide" toward the bottom of the bowl, their brake lights don't come on! If they stood on the brakes like an out-of-control Prius, they'd likely flip or roll the car or cycle.