Yes, with a bit more depth to the reading, you'd know that the robber had already collected the money and was leaving when he was shot in the back.
And what happens when another do-gooder walks into this taqueria, sees this guy shoot someone, and then grab money off the body? Wouldn't that person be in the clear to shoot the first guy?
What if the 2nd guy is a police officer?
As for the risk that someone else might mistake the shooter for the robber, anyone who has taken a concealed carry class has learned that there are risks to defending yourself. It's a choice you make because you don't think there are better ones.
But fundamentally, I'm objecting to your characterization that this guy was looking to legally kill someone or that it was motivated out of a desire to keep his wallet. The robber was threatening people's lives. The danger was not over. Shooting the robber was a reasonable choice given what the shooter knew at the time.