Depends how much the bullet did on it's way through the side of the neck, as the various stills of the entry point are in line with where the carotid would be which explains the extreme blood loss. If there's enough of a cone of force that it takes out the spinal cord then that's possible, but that depends on the caliber and type of bullet used. Higher caliber will mean more damage, and hollow points are specifically designed to cause that kind of increasing damage as the bullets pass through an object. Firing from as far as is being reported a higher caliber would be needed so the spine being damaged enough could explain the physical reaction, but then the right vagus nerve and other parts would have been hit at the entry point so it may not be as simple as the spine.