Non-profit status is nothing secret. If a company does not make a profit, they can get non-profit status. The NFL along with thousands of other businesses are not creating a profit and have entered into this agreement with the USA.
The NFL really doesn't create a profit. Individual teams do. That's what people often forget and overlook. But even then, if a team really wanted, they could also reach non-profit status by simply not creating a profit.
Frankly, I believe more companies should do this. It would actually generate more tax money through income tax rather than corporate tax and it could even add additional jobs to the labor market.