In the 1920's the NFL switched from being classified as a sport, to being classified "entertainment".
With all "sports", like boxing for example...there are rules and commisions to make sure those rules are followed.
With entertainment, its a free for all. No rules and EXACTLY like a Broadway play, you can make your entertainment as realistic or cheesy fake as you want.
The NFL has chosen to make it appear real by having announcers narrating and refs making sure "everything is legit".
But to answer your question above...When a person or group decides to start a company, the state asks what "Category" will the company fall under.
Just a few examples...Construction, healthcare, entertainment, lawn care and MANY MORE. Its an almost endless list due to subsections.
So the NFL simply clicks the entertainment section and they are off and running, its all a play, they can do what they want