This has been discussed before, and while technically it's true, it's misleading to a large extent.
The NFL as an organization is tax-exempt, but that doesn't mean the individual franchises are - they're not. And virtually all of what would be profit is either generated at or funneled down to the individual franchise level.
The league’s tax-exempt status became a talking point during the 2011 lockout, with NFLPA Executive Director DeMaurice Smith repeatedly chiding the league regarding a label more commonly associated with charities. The league’s position was, and is, that all money flows through the league office to the teams, and the teams pay the taxes. That’s what NFL spokesman Greg Aiello told CNN.com in response to Coburn’s contentions.
Here’s the reality. The NFL fits within the current legal definition of a non-profit business association. If the IRS disagrees, then the issue should be litigated. And if Congress thinks that the government is getting screwed by the definition of a non-profit business association, Congress should pass a new law.