You haven't said anything about why vigilantism is wrong. You've just reasserted that it's wrong.Because it is revenge instead of lawful punishment.
Now it is your turn to state WHY vigilantism is RIGHT.
What I'm doing here is giving you a chance to demonstrate that you have thinking that's deeper than "Vigilantism is wrong." If can explain in some detail, then we can see whether or not it's still wrong in the current circumstance.
But it seems like your brain is stopping at "Vigilantism is bad." and considering that to be "job done".
What if society is so small that laws are not defined? What if the laws are fundamentally unjust ("Left handed people are evil and will be executed.")? What if the laws are fine, but the justice system is utterly corrupt and those with power can get away with murder? What if the method of determining guild or innocence is fundamentally flawed, and evil people are being let free, while innocent people are being convicted? All of those are questions that you should be able to answer if you've thought carefully about it.