This is the way

I actually looked into this recently. It’s related to standard naming conventions established by England. Originally there was Association Football (soccer), gridiron football (American football) and rugby football (obvi rugby). Regarding American football,

“Both soccer-style football and rugby-style football eventually found their way to America. What resulted was an American combination of the two games. It wasn’t until much later (1906) that forward passing was allowed. So because the American game was really just another form of the European football games, it too became known as football.”