That is correct. Similar to how the English word "ballplayer" is defined as "a baseball player" in North America. Every country/region has its preferred default ball game.
For Americans, it should also be noted "football" in this context is referring to "soccer". In many countries outside of the U.S. "American football" is defined as "American football", such as the term "fútbol americano" in Spanish, where "fútbol" by itself is "soccer". This is to differentiate the terms because soccer is far more popular than American football internationally and the majority of English-speaking countries refer to "soccer" as "football".