If you watch the film or look at the photo sequence posted, you can see that JFK actually dips forward at the impact of the bullet, then recoils back.
Bullet impact will not move a man sized target much. I've shot Jackrabbits with large caliber rifles delivering over 3,000 ft/lb of energy. They rarely move much parallel with the bullets path. There will be a large pattern of spray around the impact area.
What the photos and the film show is a shot from the rear.