Americans, Canadians, Australians, and even the Irish have their own local games that they refer to as football. That leave the UK and...possibly Jamaica?...as English-speaking countries where Association Football is unambiguous described as just "football". Sure, you can point to all the Spanish-speaking countries in the world that call the game "fútbol", but we're discussing the English word here, so it's reasonable to limit our survey to the Anglosphere, and there, you're wrong.
(Granted the term is fully ambiguous in Australia and Ireland, where a reasonable percentage of the population will assume Association Football if you just say "football", but a reasonable percentage won't.)
And even in the UK, the term has been redefined. It used to be (and in some sense, still is) a class of games, which is why Association Football even has that name. England alone has at least three games that were once all described as football, including Rugby League and Rugby Union. Blaming Americans for redefining the term every country has redefined seems a bit misguided and historically ignorant, and borders on hypocrisy.