Goth is one of the dumbest subcultures around. That said, I doubt being goth had anything to do with this guy killing a woman.
It goes much deeper than wearing black.
I'd say that the fact that this kid is a goth, and the fact that this kid killed the lady, are all part of the same package. The goth subculture did nothing to dissuade, and probably a lot to encourage, him to act out on his urges.