Leaving aside the issue of whether this guy was qualified to determine if she was "already on the edge of death" or could be saved if transported to a hospital, what right did he have to "end her suffering"? Shooting someone to "end her suffering" is clearly murder under Minnesota law (and in every other state):
609.19 MURDER IN THE SECOND DEGREE
Whoever does either of the following is guilty of murder in the second degree and may be sentenced to imprisonment for not more than 40 years:
(1) causes the death of a human being with intent to effect the death of that person or another, but without premeditation.
Does not mean that I feel the law is correct, has justice as its basis, or that it exonerates the two thieves in the slightest.
As I stated earlier... They started it by breaking in with intent to burgle. If he'd gone full Ted Bundy on them, I'd have charged him with mistreatment of human remains, but not murder.
That's me though. I fully admit I'm a cold hearted bastard on a few topics. I firmly believe that if you initiate a crime against another person, that whatever punishment they meet out to you at the point of your offense is about as "just" as it gets.
Whatever the law may do to Smith is at best a side point. The two thieves got what they deserved.