You do realize that a nuclear war, with thousands of nukes, would single handedly knock out a chunk of the population, not to mention other weapons than just nukes, like invasions of other countries. Other countries would invade, kill civilians, etc. The world would most likely end if a country like the U.S. or Russia went into a full out nuking war (highly unlikely, but still)

The war that would end the world would most likely be over water, or oil, or something. There wouldn't be a random "lets go nuke every fucking country" approach.