Your challenge, should you choose to accept it, is for the Non-Aligned Movement to win the Cold War in a manner decisive enough to be comparable to how the USA is seen to have won the Cold War in OTL. This is to be done without nuclear war.
The NAM wasn't really an alliance or even a movement like NATO or the Warsaw Pact. On the one hand, you have Mexico and other pro-American nations. On the other, you have China and other pro-Soviet nations. An you also have arch enemies India and Pakistan, Iran and Iraq. The only way this could work is if the NAM acted as a unified force and was determined to maintain peace. The Americans were pro-freedom, the Soviets pro-equality and a third, "good" force could be peace
Well, I did use the overall "good" ideals that each side was fighting for. Not all American allies were free, but America promoted freedom. Not all Soviet allies, and certainly not the Soviet Union itself, were "equal", yet that's what they championedYour definition of freedom is strange.
Do you mean freedom to overthrow democratically elected governments and replace them with brutal but US-friendly dictators?
Anyways, a Non-aligned movement "winning" the Cold War would be impossibly-hard to achieve, as others have said due to the fact that it's so diverse, it was split by the Soviet invasion of Afghanistan because they couldn't decide wether to condemn it or support it.