The etymology section of your link suggests different:
The demographer, anthropologist, and historianĀ Alfred Sauvy, in an article published in the French magazineĀ L'Observateur, August 14, 1952, coined the termĀ third worldĀ (tiers monde), referring to countries that were playing a small role in international trade and business.Ā His usage was a reference to theĀ Third Estate, the commoners of France who, before and during theĀ French Revolution, opposed the clergy and nobles, who composed the First Estate and Second Estate, respectively (hence the use of the older formĀ tiersĀ rather than the modernĀ troisiĆØmeĀ for "third"). Sauvy wrote, "This third world ignored, exploited, despised like the third estate alsoĀ wants to be something."
But you're right in that the term began to be used far more widely during the Cold War for political alignment.