The NFL Game Pass app was launched for Apple devices on August 1st, 2017. This Apple app is available for NFL Game Pass users on iPhone, iPad and newer versions of Apple TV.
Due to global app-update restrictions set by Apple, the new NFL Game Pass app is only available to those on Apple TV (4th Generation and 4K). This is a restriction that Apple have set to all its providers who attempt to update their apps, rather than specific to NFL Game Pass.
Users of Apple TV version Version 3 or older can still use the Apple AirPlay feature from their iPhones/iPads to enjoy NFL Game Pass on their Apple TV.