Johnson himself explained it quite well in an essay entitled “Cold War Chess” (PDF version here) for Prospect:

 

“Chess has always been a simulacrum for political and military confrontation, with its gambits and endgames, stalemate and checkmate. We imagine diplomats or generals facing each other across a board. The game has been internationally popular for more than two centuries, but, like the literary genre of the spy thriller, it came into its own in the cold war. ... And in real life, it was the Fischer-Spassky match of 1972—when an eccentric American genius smashed 25 years of Soviet chess hegemony—that marked the beginning of the end of the cold war.

 

“Chess provided a mega-metaphor for this psychological war, one that derived added significance from the game's important role in Soviet communist society. The Russians might have lagged behind in military technology or economic competition, but over the chessboard they reigned supreme. A battlefield that for the first time in history was genuinely global could be metaphorically translated on to the 64 squares.

 

“Chess provided one of the safety valves that kept the lid on the cold war. But how did chess come to play this role: both symbol of the war and its antithesis? And how does chess illuminate the process by which the west triumphed over communism?”

 

If you would like to learn how Johnson answers these questions, by all means buy the book. You can read an excerpt of the book here, or view a preview of the book here.