Also watched the video, that description is not accurate.
The officer attempts to open the driver's door. The driver holds onto the door with his left hand to keep it shut while starting the ignition with his right. The officer yells "stop", leans into the car to grab the driver by the shirt / seatbelt with his left hand and immediately shoots the driver with his right hand.
The whole escalation is very fast. It's less than three seconds between the driver starting the ignition and the officer firing. Based on where the officer is standing there's no way he could have been injured by the car.