Coincidentally, or not, a lot of these countries are located in the tropics, where global warming would probably have its most pernicious effects. True, they would probably not be entirely eradicated even under some of the worst-case, fattest-tail climate change assumptions.
I'm not exactly sure what mechanism Jim Manzi had in mind for the mechanism of GDP decline, but I'm not exactly sure I also don't suspect that I'd find the tropics to be most effected in terms of GDP. In terms of total damage, or lives lost, perhaps.
Given that the solution to global warming in general is increased sustainability (broadly speaking, of course), and that energy sustainability will have not only the environmental effects but the infrastructure effects, failure to implement such sustainability measures will have an even greater effect on GDP on those places where fossil fuel energy is used most, in the most industrialized nations, not the bottom-rung-of-GDP nations that Nate selected. But, then again, maybe Manzi ignored these effects entirely.