I can't say I'm NOT glad that asshole is dead.
I can't condone murder, either, though.
What's right isn't always legal and what's legal isn't always right. I think laws against vigilantism exist and persist for VERY good reasons. Not every case is this cut-and-dried--with incontrovertible video proof. The next father might not have such horrifying evidence. He might have suspicions that turn out to be unfounded or mistaken. He might be WRONG and kill a person over a crime of which they are innocent.
That's why vigilantism is illegal and punishable.
So, I will never condone murder for any reason (self-defense is another story and there's DEFINITELY an argument here for that, if the father has an even halfway decent attorney ... it wouldn't even be a long-shot, Hail Mary-play). The slope for giving folks passes on committing even small crimes is a slippery slope for whole communities and society.
All that said, I think that if the father gets charged with some degree of murder and found guilty ... his sentence should be: time served, a fucking medal, and a ride home in a Rolls Royce that's led by a parade.