Zero Sum Games & Nuclear War?

 In a recent article in the Guardian on a wargame conducted recently to investigate tension between Russia and Finland a reference  was given to a paper by Roger Mason [1]. This paper was all pretty standard stuff on the history of wargaming, but we have this at the start of the section covering the Cold War:

The cold war offered strategists, political leaders, and wargamers a new set of  problems. The challenge was the new age of nuclear weapons where strategic warfare might truly be a global zero-sum game.

This left me wondering exactly what did the author think or intend this "zero-sum game" phrase to mean in this context?

Lets look at the definition of a Zero Sum Game, here from Wikipedia:

Zero-sum game is a mathematical representation in game theory and economic theory of a situation that involves two sides, where the result is an advantage for one side and an equivalent loss for the other.^[1] In other words, player one's gain is equivalent to player two's loss, with the result that the net improvement in benefit of the game is zero.^[2]

 What would a zero-sum pay-off matrix for strategic nuclear war look like!? There seems to be a couple (or more) possiblities behind this quote: 

1. I don't understand what the author is getting at,

 or (more likely)
2. The author does not know what a zero-sum gave is, and is using the phrase because it makes him sound smart.

References

Mason, Roger, Wargaming: Its  history and  future, The International Journal of Intelligence, Security, and Public Affairs, V20, 2 pp 77-101, 2018.