This is wrong.
Soccer was (by Americans) called Soccer after the word ‘association -> assoc -> soccer’ because back then it was called ‘Association Football’
Football is an umbrella term for sports which was not mounted (by foot) and used a ball so ‘by foot with ball -> football’
So after that to call American Football, Football, is by definition not wrong but misleading for most parts of the world.
More precise would be ‘American Rugby’ since American Football is a derivative of Rugby much more so then of European Football.
