Dr. James Gilligan, a retired psychiatrist out of Harvard, spent his life studying murderers and why they did what they did. Sometimes they engaged in mutilations of their victims - like flying planes into mountains, the way this German pilot did.
What Gilligan found, in every case, was that the perpetrators suffered from unbearable feelings of humiliation, which they attempted to erase by killing people. He found many of them had fantasies of going out in what they considered "a blaze of glory," taking as many people with them as they could.
He said if you wanted to understand why people murdered, then look at the story of Cain and Abel. Feelings of humiliation followed by revenge. Murder.
As for trying to shove these people in boxes of "Beta rage" and "Omega rage," go right ahead. You're wasting your time, and you'll never understand why this guy did what he did.
You're better off understanding what Hubris is (the Greeks considered it a form of grandiose insanity, in which the sufferer cannot tell the difference between right and wrong). The Bible calls it Pride. And what follows them? Nemesis...destruction.