While the actual bullet impact on the stag is real the rest of the video is obviously a compilation of film. The camera is in front of the shooter and guide for some frames, probably staged after the shot and then again the camera is at the fallen animal as the hunter and guide approaches, the guide with a handgun out ready for the coup de grace if needed, obviously a staged approach. Most of the other filming of stags is not necessarily related to that hunt.

The rifle muzzle has had the slot modification done to it (can't recall the correct name for it at the moment) but the guide would have a burst ear drum if the rifle was fired over his shoulder in that condition.

While red stag can be curious and aggressive when in the roar (rut) they will take off quicker than any animal once they identify danger.