In Germany (one of the countries with long standing football tradition) it is called "Fußball" which splits into "Fuß" (foot) and "Ball" (ball). It makes much more sense than calling "American Football" Football, as in "American Football" the feet are less dominant than in "soccer" (where hand usage is actually a foul).
The name soccer came from Britain, not the US. It was used to differentiate Association Football (soccer) from Rugby Football (rugby). Ireland, South Africa, Australia and New Zealand all still call the sport soccer. Even in England, it continued to be a popular name for the sport until the 1950s.
Correct, and most native English speakers are American. That doesn't even account for Canada or Australia where it has also traditionally been called soccer.
The fact that the "F" stands for "Football" in the name of an organization with a French name seems irrelevant.
I don't think many people likely to be interested in an association football API call it "soccer". They're marketing to that audience, not the minority of the world that assumes "football" refers to a gridiron sport.
Because any good developer should, when presenting a product in an international market, consider i18n (which involves more than just "translate from language A to language B").