He's lucky that buck wasn't more aggressive. I'm afraid I wouldn't have had the restraint he had, that buck would have been dead within the first minute, the video would be unquestionable evidence of self defense.
I would have at least fired one off into the dirt to try and scare him off. If that deer wanted too he could of really hurt that guy. Possibly that deer has had alot of human contact or is being fed by someone local. I've seen deer around my area a long time ago come out of the woods and eat from a persons hand.