Technically, every country in South America is considered a part of Latin America except British Guyana, Suriname, and France. Not including islands like the Malvinas or the ABC islands, of course.
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I should have specified one single flight. Of course you can fly to Dubai from São Paulo and then to Seoul or to Sydney from Santiago and then on to Peking.
But direct flights are very limited.
French Guiana?
Well, sort of. Looking briefly at many maps of France (in French), the inclusion of the DOMs are relatively rare, in contrast to the inclusion of Alaska and Hawaii on most US maps. Corsica is about as prevalent as Alaska and Hawaii (probably more so), while Guyana and the other DOMs are about as prevalent as Puerto Rico.
I also don't know that excluding French Guiana from "Latin America" is actually correct anyway. French is a romance language.
Are the countries on the continent of South America not generally considered a part of Latin America? Because there are other options from Santiago, Sao Paolo, Rio, etc. to Tokyo. Some of the options are on Air Canada, with a stop in Toronto which avoids U.S. airports but presumably not U.S. airspace so there may still be some additional scrutiny at departure.
You don't actually have to go all the way to a South American city, Panama City has Air Canada flights to Tokyo. It looks like the other carriers (Emirates, KLM, Turkish Airlines) have stops in a South American city first. The Air Canada flights aren't much more expensive but the European & Asian-based carriers are much more expensive than the flights with stops in the U.S.