I think the guy was a whackjob and just shot Kyle so he could say he shot the baddest a$$ sniper there ever was. Nutcases don’t need a real reason to engage in stupidity.
Story in the article about him attacking and injuring two fellow soldiers for no reason.
Analyzing a nut is pointless. He had a history of violently attacking people he thought were making him the butt of a joke. My guess is that someone made a goodnatured joke like vets do,, and he started shooting. And he supposedly was very paranoid.
Out there in the middle of nowhere, for no reason we can know, he might have decided he was going to be killed and shot them first.
Might as well try to understand Son of Sam and his talking dog, or Hinkley shooting Reagan to impress Jodi Foster.
That is what I think too. Seeking attention by killing a hero.
I believe you are correct. The guy is quite apparently unstable to put it mildly.