Two blocs are emerging. One is largely unified around shared cultural interests in resilient democracy and defence of human rights. The other is a hodge-podge of malcontents, allies-of-convenience and one strong but largely regional power (i.e. China).
If we look at this as a political struggle then we have to look at the problem-solution ledger to see who holds the advantage.
The US (and the West) have issues with an imbalance of power and wealth, and growing numbers of disillusioned, young voters - this is the problem statement. What is the solution that the non-aligned movement can offer? Worse inequality? Fewer rights? What?
The non-aligned countries have fractuous political bases and are shoring up their systems by cracking down on dissedents, attacking neighbours and attempting to corrupt other nation's foreign policies. No one is lining up to migrate to these countries, no one is holding them up as a beacon of rightousness (outside of the wingnut extremes, of course).
Contrast this to the Cold War. The Soviets held a significant sway over the "International Left". They had answers to the problems of the West. Not good answers, but good enough to sway a lot of students and intelligentsia.
China has no allies of note. Russia is a basket case. The rest of the non-aligned bloc are essentially local dictators trying to keep the pin in their respective grenades. All of them are experiencing the same struggle of either a rapidly aging population with no migration, or a rapidly growing youth who want a better life. For example, China's median age is rising 6 months for every year that passes, and they are a long way from being a sustainable, powerful economy.
These are interesting times in the political sense but unless the West starts kicking a lot of "own goals" - which is very possible but not exactly probable - then the US (and to a lesser extent the EU) will own this century as well.