he felt that he was no longer human, and so people could construe that as he has a vendetta against them.
Except that the whole event plays out more like a temper tantrum. If he no longer thought of himself as human, he wouldn't care about humanity or what we do to each other, which would result in one of two events taking place: Either he kills everyone or simply leaves. Killing only some people and then leaving doesn't make any sense. Who is he warning and why if he doesn't have a clear connection to us? If he's angry, he's gotten his revenge and left, the matter is resolved. If he's concerned about humanity's ability to police itself, why did he not just take over or kill everyone instead of just a few?
Plus, as I stated before, this threat of Dr. Manhattan does not necessitate global cooperation. He is a single enemy who cannot be fought through conventional means, so there isn't any reason the countries of the world need to pool their resources for a possible conflict.