Why does it matter if it personally occurred to him or someone related to him? It happens to plenty of people. You can have empathy for people not bound by blood.
There is a great deal of injustice in the world. Psychologically healthy adults have learned to add a reflection step between anger and action.
By all evidence, Luigi is a smart guy. So one can only speculate on his psychological health, or whether he believed that there was an effective response to the problem which included murdering an abstract impersonal enemy.
I'm stumped, honestly. The simplest explanations are mental illness, or a hero complex (but I repeat myself). Maybe we'll learn someday.
He could die quietly making no impact on the issue. Or he could sacrifice the rest of his free life to put a spotlight on the issue. That is what he chose to do. Not an easy decision I'm sure.
But that doesn't seem to be true at all. He just had a whole lot of righteous anger, I guess. Gotta be careful with that stuff.