What law did he break?
The intentional taking of the life of another is not authorized by section 609.06, except when necessary in resisting or preventing an offense which the actor reasonably believes exposes the actor or another to great bodily harm or death, or preventing the commission of a felony in the actor's place of abode.
https://www.revisor.mn.gov/statutes/?id=609.065
I don't think a reasonable person believes someone unarmed and dying in front of you is a threat of death or great bodily harm-if he believed that, he probably wouldn't come as close as he had to to deliver a 'kill shot' under the chin
Felony? it depends on the value of what they were stealing. (At least that's what was taught in police academy way back when.) I'm sure burglary laws have changed since then. I do rememeber that burglarizing a garage VS the house would result in lesser charges...UNLESS the garage was equipped with a bed(and maybe a toilet) that got used now and then. Then it could be considered an 'abode' or 'dwelling' and treated equal to the house.