In a 2011 New Yorker profile of Norwegian chess champion Magnus Carlsen, D.T. Max digresses to explain the logic behind the Soviet interest in chess:
“Lenin, an enthusiastic player, made the game a priority for the new nation. In 1920, Alexander Ilyin-Zhenevsky, a commissar of Soviet chess, wrote that chess, ‘in some ways even more than sport, develops in a man boldness, presence of mind, composure, a strong will, and, most important, a sense of strategy.' The Soviets set about mass-producing chess excellence. In 1991, the year the Soviet Union broke up, the top nine players in the world were from the U.S.S.R. By then, Soviet-trained players had held the world championship for all but three of the past forty-three years. The Soviet program emphasized focus, logic, and, above all, preparation. The board was an informational battleground, and work put in before the game allowed you to see chances that your opponent might miss. The Soviets’ foremost chess practitioner, the world champion Mikhail Botvinnik, was also an electrical engineer. ‘Some experts say my principal strength is my zest, my aggressiveness,' he once said. ‘I think it’s my scientific training, the logic of a scientist’s search for truth.' The directors of the Soviet chess program accumulated vast archives of opening moves, as well as records of the play of foreign opponents. The data gave them a significant advantage, but decades of Soviet dominance also led to complacency and a reliance on received wisdom.”
In short, “The Soviets thought that training a generation of chess players would compensate for historic flaws in the Russian character.” From the Soviet perspective, nothing was more threatening than an eccentric Western genius like Bobby Fischer.