It won't be the end of humanity... There's no chance that this will ever develop to that scale.
War is an archetypal situation. Once the possibility of one starting develops, it has "suction": people react to the archetype, and that threatens to overwhem rational thought. The archetype was worshipped as a divinity in many cultures precisely because war behaves as if it was a living thing seeking to devour people - or, in this case, the entire world.
So yes, there's every chance this will develop into World War III: Last Dance.