I'm a firm believer in self-defense, but to leave to get another gun and return to shoot an attacker who is no longer a threat is a real stretch.
I agree there are two stages in this incident. Taking the attacker out of action, including killing him, is self-defense. The five follow-up shots appear to have been not called for. To say that was murder may or may not be technically correct, depending on further determination.
It is considered that if you have cause to defend yourself with a gun (or any other weapon) you have the right to kill the attacker. It is not uncommon to fire multiple shots until the attacker is stopped. In fact, it is recommended because a hesitation between shots could be fatal for the defender, and that includes law enforcement personnel. There is even a school of thought that says if you shoot, you should shoot to kill. However, and it's a big however, once the threat has been stopped, dead or alive, the act of self-defense also stops.
Did the robber deserve to die? My belief is that once you decide to commit a crime, you deserve the consequences. Consider it a bad career choice.