It depends on whether a church is considered an establishment under the
law. An establishment is usually a store or something of the like that is in business for a profit, unlike a church. If a church is an establishment, and the church is over 2000 square feet, then the game can't be shown on more than 4 TVs (1 each per room) no larger than 55 inches diagonal. If they are not, then the game can be shown on a TV of a kind commonly used in homes. In both cases, they can't charge a cover.
The NFL was overreaching. They seemed to want to limit churches to 1 TV of less than 55 inches. That's not what the law says - it's either allowed up to 4 TVs (1 per room) of up to 55 inches, or 1 TV of a size commonly used in homes, which theoretically could be larger.
The NFL's claim that their program couldn't be used as part of some broader church program that delivers a message simply has no basis in the copyright laws. If it did, then Algore could stop you, me and other FReepers from getting together (without charging a cover) to ridicule his crappy movie if it's ever shown on TV again. That's just ridiculous for something shown on the public airwaves.