The saying 'Kill'm All and Let God Sort'm Out' is not just military bravado. You take no chances in battle. When you are involed in a fire fight you make sure any enemy combatants behind you are dead. Injured enemy combatants are just as dangerous (if not more so) than non injured. If you do not have time to secure the prisoner you shoot and kill him.
My uncle was in the Guadalcanal campaign. He once told me that they would go to all downed Japanese and cut their throats to make sure.
Better to be tries by 12 than carried by 6.
Judging by the video (appearances could be deceiving), there's no evidence to suggest he wasn't secure. It almost sounded like the other soldier shouted "Wait!" when the marine fired. This may just be a case of someone who was suffering post-traumatic stress (after being shot and wounded himself) and couldn't exercise clear judgment.
Anyway, it's hell to be in these guys' shoes.