A gridiron football is still clearly a ball in function, even if not spherical, just like how a rugby ball is still called a ball.

The word "football" has been used to describe games played without kicking for centuries. A possible etymology is that it means not a game played with the feet, but a game played on foot. It could describe any of the games played by peasants, as opposed to the equestrian sports (racing, polo, dressage) played by aristocrats.