In much the same way that rich societies exported their pollution to developing countries, the societies of the highly-developed world exported their conflicts. They were at war with one another the entire time—not only in Indo-China but in other parts of Asia, the Middle East, Africa and Latin America.
The Korean war, the Chinese invasion of Tibet, British counter-insurgency warfare in Malaya and Kenya, the abortive Franco-British invasion of Suez, the Angolan civil war, decades of civil war in the Congo and Guatemala, the Six Day War, the Soviet invasion of Hungary in 1956 and of Czechoslovakia in 1968, the Iran-Iraq war and the Soviet-Afghan war—these are only some of the armed conflicts through which the great powers pursued their rivalries while avoiding direct war with each other.
When the end of the Cold War removed the Soviet Union from the scene, war did not end. It continued in the first Gulf war, the Balkan wars, Chechnya, the Iraq war and in Afghanistan and Kashmir, among other conflicts. Taken together these conflicts add up to a formidable sum of violence.