First, I think this shooter needs some training and/or range time to improve their shooting.
Second, IF you are going to shoot an 'unwanted" in your home, make sure it incapacitates them.
Third, once the confrontation is broken off by the 'unwanted', don't go chasing them. You become a prime witness, able to describe the 'unwanted' to law enforcement. Let them do the chasing and arresting, even if the suspect is bleeding to death in an emergency room.
Now, for my opinion: First shot or shots good, ANY shots after chasing the suspect are BAD. Could be looking at murder here, but may plead down to something like manslaughter or assault with a deadly weapon. I certainly do not want to be in this person's shoes.