Not an accountant but there are different kinds of nonprofits, OpenAI is a 501c3 (religious/charitable/educational) whereas the NFL was a 501c6 (trade association).
Obviously we all think of the NFL as a big money organisation, but it basically just organises the fixtures and the referees. The teams make all the money.
If you want to be pedantic, in legal terms, no, the NFL is a big money org ($13B+/yr in revenue, with a commissioner earning $65M/yr).
They pay dividends to the teams, however, yes. But all that revenue (which is distinct from team revenue) is actually legally earned by the NFL itself.
Obviously we all think of the NFL as a big money organisation, but it basically just organises the fixtures and the referees. The teams make all the money.