From reading the article, I get the sense that the best thing working in our[1] favor was having a series of relatively steady, not crazy hands on the nuclear football, on both sides. It's still incredibly frightening that the annihilation of the human race was literally placed in the hands of two people at any given time, but a testament to the capability of the Soviet Politburo and the American political system to…
Realistically, human civilization would still have survived a full scaled thermonuclear exchange during the height of the Cold War. Things would not have been great, but humanity would still have survived.
I am also not to sure, if they (the remnants) would survive for long with global climate change and radioactive fallout everywhere.