I don’t really think speculation about who will “dominate” this century is a great way to think about things. Almost certainly in 2079 the United States of America will have less relative power than it does today, and that will almost certainly be a good thing—it will be because people in China and India and Brazil and Indonesia are richer and because Europe continues on a path of peace and integration.
I'm really unsure about this. He's always a fairly optimistic fellow it seems, and I certainly am rarely accused of this. But for someone who writes about climate change not infrequently, Yglesias seems blind to connecting that discussion with his more general thoughts about foreign relations. That's a nice scenario he paints there, but it totally ignores the reality of drought, water shortages, food shortages, wars over resources, declines in oil, hafnium, and other key elements of economic and technological growth, deforestation, rising sea levels and the displacement that will cause, and a number of other environmental problems likely to get in the way of this rosy future he sees.
He may be right that the U.S. will hold less power in 70 years than it does now; in fact, he probably is. But I don't think that's because other nations will continue to rise in a peaceful manner. Rather, I think it's because the U.S. economy and U.S. mentality will struggle greatly with shortages in ways that other nations might now and that this will likely lead to long-term instability in the U.S. that other nations will be able to exploit, particularly either nations with long-term cooperative arrangements and generally progressive leadership (i.e., Europe) or totalitarian regimes with few qualms about doing what they have to do to stay in power and express that power on the international stage (China).
As for the developing world getting richer, given that Brazil, Indonesia, and any number of other countries rely on unsustainable resource exploitation to grow their economies, how is this going to continue when the wood and the minerals are gone?
Maybe I'm too pessimistic, but I think this scenario is a lot more realistic than what Yglesias offers, moreover I think we are already seeing it begin in Americans' struggle to deal with the financial collapse.