Update: Keep down-voting all you want. The Forbes article is weak in classifying all of the NFL as one entity. The below link gives a good overview of the structure of the NFL and it's tax exceptions. I'm glad I read it. That said the NFL still shouldn't be a non-profit organization.
http://www.todayifoundout.com/index.php/2014/01/nfl-tax-exem...
The NFL is an industry association; it exists to further the health and welfare of its industry (American football). Furthermore, the NFL doesn't take in revenue at all; it runs at an operating loss. Instead, NFL Ventures (which is a for-profit corporation) collects all monies related to the league and passes that money along--less a (taxed) retained cushion--to the teams and the teams' ownership, which are likewise taxed as per normal for-profit entities.
So, yes, your claim is misleading and your defense of it worse.
Almost. They exist to promote their part of the industry. They don't exist to support football generally and take many steps to put down possibly competitive leagues, such as using tricks to forbid players from moving to other leagues, even after their NFL careers are over. (Most commonly via delayed salary benefits that end should the player start with a non-approved league or if they speak out against the NFL.)
Update: Keep down-voting all you want. The Forbes article is weak in classifying all of the NFL as one entity. The below link gives a good overview of the structure of the NFL and it's tax exceptions. I'm glad I read it. That said the NFL still shouldn't be a non-profit organization. http://www.todayifoundout.com/index.php/2014/01/nfl-tax-exem...