Sa person killed multiple innocent people, many of them children. The father of one of those murdered children goes after that person, and kills that person. Is that justice or revenge?
It's definitely revenge, but I wouldn't call it justice as such.
Justice is the sole purview of the State. Justice comes when a criminal is convicted and sentenced according to the LAW. If we start letting random people on the street execute those who have wronged them whenever they want, that's not justice. That's anarchy. That's mob rule.
I mean, even the fact that Dexter Morgan only killed people who deserved it (if he ever made a mistake and killed a truly innocent person, I'm not aware of it) doesn't make it right. It doesn't make him the good guy. Only the State determines who deserves to be punished, and only the State determines the manner of that punishment.