To be clear, there are significant differences with the legal classifications of various non-profits. 501(c)(3) is much different from 501(c)(6) (the NFL is (6)) I am not a lawyer so I don't know what the differences are, but it's possible/likely that if someone was going for a different kind of non-profit the rules would change dramatically, so they can't quite be compared apples to apples.
So I was curious about this and looked up some more information on it (the NFL tax exemption).
Section 501(c)(6) of the Internal Revenue Code provides for the exemption of business leagues, chambers of commerce, real estate boards, boards of trade and professional football leagues, which are not organized for profit and no part of the net earnings of which inures to the benefit of any private shareholder or individual.
see: https://en.wikipedia.org/wiki/501(c)