The kids are white and he's white, so this story will go away quickly. In addition to that, the guy has been very forthcoming with his motivations, so he's not leaving many questions un-answered. There really appears to be no mystery here other than whether (a) anyone really had broken into the guy's house in the past and (b) whether it was these two. So, my analysis here comes with the caveat that it's based on the facts as they're presented right now, obviously my opinion could change as more details come out.
In my completely non-expert opinion, the (likely) applicable Minnesota statutes for authorized use of force and justifiable taking of life read:
609.06 AUTHORIZED USE OF FORCE.
(4) when used by any person in lawful possession of real or personal property, or by another assisting the person in lawful possession, in resisting a trespass upon or other unlawful interference with such property; or
So he's authorized to use force in resisting the trespass according to that law. Question remains as to whether killing them was reasonable force to resist the trespass or if a lower level of action would have done the job sufficiently. Need more facts to argue either way. But based on what he himself has confessed, it sounds to me as if killing them was unreasonable force. So if I had to make a (non-expert) argument defending him, I'd say that shooting the first individual when he saw his hips would be reasonable. PARTICULARLY because seeing their hips might indicate that he was trying to inflict a wound on the lower half of their body, leaving less risk of inflicting a mortal wound. Waiting until he saw their chest and head could indicate that he intended to kill them from the beginning. If I could argue that he intended to shoot them in the lower half of the body to incapacitate them and stop the crime, I'd guess we'd have a pretty good shot to demonstrate reasonable force.
To continue on to the next part of the authorized use of force sub-division.
609.06 AUTHORIZED USE OF FORCE.
reasonable force may be authorized...
(5) when used by any person to prevent the escape, or to retake following the escape, of a person lawfully held on a charge or conviction of a crime; or
Again, shooting them below the chest seems to be an easy reasonable force argument. It would be reasonable to expect that to stop their escape. What seems to me to be an added wrench, is that neither of the teens appeared to have been attempting to escape or even physically capable of escape after the first shot(s). I'm guessing (5) doesn't help them very much here, because preventing escape may have been moot.
The next (likely) applicable statute:
609.065 JUSTIFIABLE TAKING OF LIFE.
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.
If ONLY the first part of that sentence existed, "when necessary in resisting or preventing an offense which the actor reasonable believes exposes the actor...to great bodily harm or death," he might not get off. Reason being, the prosecution would probably demonstrate that by the time he killed them, he wouldn't reasonable believe he was exposed to bodily harm or death. They didn't have any weapons and it sounds as if they were completely incapacitated by the first shot(s). HOWEVER, the second half states, "or preventing the commission of a felony in the actor's place of abode."
At this point, it becomes cut and dry in my opinion legally. They were committing 2nd degree burglary which MN law defines as:
609.582 BURGLARY.
Subd. 2.Burglary in the second degree. (a) Whoever enters a building without consent and with intent to commit a crime, or enters a building without consent and commits a crime while in the building, either directly or as an accomplice, commits burglary in the second degree and may be sentenced to imprisonment for not more than ten years or to payment of a fine of not more than $20,000, or both, if:
(1) the building is a dwelling;
Their crime satisfies the second degree burglary definition and is thus a felony. Statute 609.065 JUSTIFIABLE TAKING OF LIFE authorizes an individual in their place of abode to take a life if it prevents commission of a felony.
That's what he did. And that's why I think he'll get off.