I think Stewart lifted off the throttle momentarily, based on the moves of the car in front of him. In a sprint car on a dirt track, lifting off the throttle will make a car drift to the right, higher on the track. Steering correction in those cars depends on throttle, so Stewart tried to reverse his rightward drift by giving the car more throttle, too late.
Compared to other oval-track racing, Sprint cars are under tenuous control. I can't imagine a worse place to get out and play in the traffic.
I thank you for your civil response. I have to say that the other cars did not use throttle when they were near (although not as near) Ward. Also I would assume Stewart who is a champion would be more than enough of a competent driver to correct his car in the direction he wished it to go. But not only did it not take him to the left or keep him going straight, his supposed correction led him right into Ward. And that to me is hard to swallow.