reaction vs action
I might agree that the typical conservative reaction to this story is likely to be along the lines of what you said.
What an individual would do in the circumstances would not imo be divided along political lines. I have no doubt I would shoot a robber but I can't see myself executing a disarmed and disabled robber. That might change based on the circumstances and the threat level leading to the shooting. Factors such as how many times the shop keeper had been robbed previously would also play a part.
If the person was not a robber but someone who attacked me or my home for a grudge or vendetta I might be very tempted to finish the job.