His question is what law gives the NFL this right. You can't just claim "I own" this.
As far as I know I am allowed to record anything I want. Perhaps not with audio, but I am not aware of any law that gives someone the right to prevent video recording.
They have the right to kick you out (if they catch you), but not to prevent recording.
The NFL leases exclusive rights to TV stations to broadcast the action.
Anyone else who broadcasts the action will get sued and shut down.