Murdering same in cold blood while he is unconscious, not so much.
I agree with that.
You keep repeating that the robber was Unconscious. The video does not show that. And even if the robber APPEARED to be unconscious, the victim did not have the medical training to know whether or not the robber was faking — because no mortal man has that ability, especially not during a stressful event like an armed robbery.
Also the victim could not know that this particular participant in an armed robbery was not himself carrying a weapon. Weapons can be concealed — it happens all the time.