Nothing is simple. Murder of a murderer is still murder. If it's in self defense then you'll be found not-guilty. If you make the first move, you're guilty. The best way to avoid legal issue if you can help it is to get the cops involved once you have the evidence that such-and-such is the person who caused the murders. Not much of a solution but it keeps you out of legal trouble. If you kill him in your home, he's trespassing and may/may not result in legal action against you. There's about a billion different ways something can play out.
As far as moral issue, yes. You can say that he murdered first. You're saving lives by taking this one. But then, now you can't justify sparing lives that indirectly caused the murders. You can't justify ignoring people who supposedly inspired people to kill, from game programmers to directors to movie actors to musical artists. And besides. It's a life that's on your hands regardless if you want it or not. It's always going to be a part of you once you've taken it. Letting them live results in more suffering later on, but killing them is unjust and should never be in the hands of a person who has a personal vendetta against them. Think Batman for example. The Joker, Two Face, Harley Quinn, Scarface, Mad Hatter, Edward Nigma, Mr. Freeze, Clayface, The Penguin. Only a small part of the universe of Gothom City, all of them killers, murderers, some tied to Batman in every way, some tied to the people he knew. Killing them would be mercy to the people of Gothom. But killing them means putting yourself at their level, giving away your humanity and sanity in the name of justice and protection.
The opposite end of the spectrum would be the Punisher. His family was killed by a gang war in the middle of a park, and he dedicates himself to basically slaughtering everyone who's committed a crime. Can you justify yourself? It's revenge, sure, but then those people were the same as you, with family and friends and hopes and dreams, however battered and shattered they may be. But then, it's always going to be open for interpretation, and someone who has their mind set isn't going to change easily. Morally, it's a terrible war you start. Justifying it becomes harder as it goes further. But some people are going to go the Punisher route regardless, and the only hope is to limit the damage they do.