Of course it does. But that money could have been generated by anything that people happen to care about -- it isn't specific or inherent to Football.
If everyone in America instead loved Jai Alai, then suddenly that person's income is no longer dependent on American Rules Football, and is instead dependent on Jai Alai. Or maybe we all loved watching Starcraft 2 matches instead. Or debating objective meaning. It doesn't matter; we could in theory have attached interest to anything. It just so happens we have attached interest to American Rules Football in our particular culture. If you looked at any other culture in history, it would be different.
There's nothing inherent in the game of football that makes it particularly or especially worth as much money as it is. Again, if people stopped caring about American Rules Football tomorrow, then the staffer's ability to make a living on it would disappear, overnight.