That's a bit misleading. Each of the teams are a for-profit enterprise and pay taxes on the huge amount of money they bring in.
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...
So, yes, your claim is misleading and your defense of it worse.
So there is a little bit of shadiness going.