There aren't enough nuclear weapons to destroy the world, not by a long shot. There aren't even enough nuclear weapons to constitute an existential risk in and off themselves, though they might still contribute strongly to the end of humanity.

EDIT: I reconsidered, and yes, there is a chance that a nuclear war and its aftereffects permanently cripples the potential of humanity (maybe by extinction), which makes it an existential risk. The point I want to make, which was more clearly made by Pfft in a child post, is that this is still something very different from what Luke's choice of words suggests.

How many people will die is of course somewhat speculative, but I think if the war itself killed 10%, that would be a lot. More links on the subject: The effects of a Global Thermonuclear War Nuclear Warfare 101, 102 and 103