jonvi
La Familia Ohana
Because that's how those cars are built. Acceleration makes them easier to maneuver and steer. It's likely that he punched the gas so that the car would be easier to maneuver away from Ward. Keep in mind also, that you can see in the video, that Ward moved to avoid the #45 car which is part of the reason that car didn't hit him. The driver of the #45 car had very little time to react. Stewart had even less time.
These quotes are from the facebook page of Mark Tychoniewicz who was part of the crew working on the #45 car:
I tried telling em. The outside tires are much larger than the inside tires. Give it gas and the car pulls to the left. Let off the gas and the car pulls to the right.