This is the story of a guy, who was acquitted of 2nd Degree Murder by reason of self-defense. The reporter still goes on about murder. It isn't murder. (That's illegal.) It isn't vigilantism. (That's illegal too.) It was self-defense, which is - even in NY City - legal.
Ann H. - one of the commenters on this story - got it right.
Homicide is the death of person at the hands of another. Death certificates have four terms for manner of death--accident (he fell out of an airplane), natural causes (she had a heart attack), suicide (he shot himself in the head) and homicide (someone else killed her). The death certificate of an executed criminal gives the manner of death as "homicide"--it wasn't an accident, natural, or suicide. The person died at the hands of another.You can read her entire comment here.
This isn't the only thing wrong with the Slate article, of course, only one of the more glaring errors.