When the leaders of China and Taiwan met last weekend for the first time since 1949, the unseen presences in the room were the ghosts of Mao Zedong, the Communist Party’s Great Helmsman, and his bitter rival, the gaunt Generalissimo Chiang Kai-shek. They had been adversaries in the Chinese civil war for more than two decades, before Mao’s victorious peasant revolutionaries took power in Beijing that year.

Chiang was driven into exile on Taiwan, taking with him his Chinese Nationalist Party, or Kuomintang. The enmity of Mao...