Any bar or commercial establishment pays cable/satellite fees based on the number of seats (not customers) in their establishment. Big sports bars pay big cable fees.
What part if any of that fee goes to the NFL, I don't know, but the TV networks definitely get a cut of it which is fair since they pay the NFL big bucks for broadcast rights.
This needs to be repeated. It's not like the NFL is giving sports bars "an exemption" and picking on a Church. The sports bars pay for the rights of the games they show.