I haven't seen the video of this yet, but if I understand what happened correctly the shopkeeper should be prosecuted. Probably not for murder but some kind of voluntary manslaughter.
You have the right to defend your life and property against threats like this, and lethal force is acceptable to do so. Nobody can argue the first shot, and if that had been the one that killed him this wouldn't be an issue. But once the guy was down, bleeding from the head and unconscious the threat is gone, and putting 5 more bullets in him basically makes it an execution. The shopkeeper is going to have a hard time arguing self defense for the second round of shots since he apparently repeatedly passed by the wounded robber with his back turned to him, and had time to go get a second gun with which to finish the kid off. As far as I know the cops did not find a gun on the robber who was killed, so once he was down from the first shot the threat was truly over.
I'm sure it's not easy to think clearly when you're actually in a situation like this, but I believe that being prepared to make the right choice is part of being a responsible gun owner.