Asked and answered several thousand times here. It shows a fundamentall misunderstanding of the word "football". The fact of the matter is that the term is simply a reference to one of any number of games in the football "code". I can think of at least eight -- American (gridiron) Football, Association Football (soccer), Australian Rules Football, Canadian Football (another variation of gridiron), Gaelic Football, International Rules (a blend of Gaelic and Australian), Rugby League Football and Rugby Union Football. No doubt there are some more. What all these games do have in common is an origin in local village and school games which where played on FOOT (as opposed to the back of a horse) and with some sort of BALL fashioned from an inflated pig's bladder wrapped in leather. Hence the generic term "football". Nothing to do with playing the ball with your feet.

No no no. Its a different game.

wouldn't that make it American Rugby Football? I can't see what the poing in adding an extra word to the title would do.

Oh Lord, please no!

They already play rugby in America, their national team is called the Eagles (go Roger Ramjet).

yes with crash helmets

Yes.