The NFL is, IIRC, a fairly bog-standard 501(c)(6). Are you think of an anti-trust exemption rather than a nonprofit status exemption? I know that MLB has the former, and I think the NFL does as well.
"IRC 501(c)(6) provides for exemption of business leagues, chambers of commerce, real estate boards, boards of trade, and professional football leagues (whether or not administering a pension fund for football players), 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."
Of specific interest is the "Statutory History" section on page four - a history of private organizations asking for exemptions.
