Short answer: the noun phrase is a condensed version of the owner of any given NFL team.
It seems like you're asking two related questions. Is NFL Owner a permissible phrase, and, if so, what might the NFL Owner refer to if it's not referring to the owner of a specific team.
First, NFL Owner can be considered "shorthand" for the "type of owner" being talked about and/or "at what level the person is an owner," namely, at the NFL level. He or she is not for example, a semi-pofessional owner but an NFL Owner
Next is the use of the definite noun phrase the NFL Owner if a particular NFL team is not under discussion (which I assume is the case given your question). The easiest approach to this is to realize that given an NFL team, any NFL team, you can talk about any of its typical "components" with a definite phrase: the quarterback, the fan base, the head coach, the owner... all these things are typical things related to an NFL team. (Another example: I can use such definite noun phrases as the front door, the mailbox, the dining room, etc of any house, once the subject of a house is broached.)
Also, note my noun phrase in the last clause of my first paragraph: ...if it's not referring to the owner of a specific team.
I can say the owner because again, given any NFL team there will be an owner (unless that position is open).