The rights for using UE4 are detailed in the UE4 EULA. It’s not clear what you mean by “show” but it seems like some kind of TV broadcast. The EULA permits that, and doesn’t require a custom license. If the use is purely linear, non-interactive (like a normal TV show), there is no royalty. Epic does get promotional rights to the material (i.e., in promotion of our engine business), and you have an obligation to notify Epic of the release.
You mention “in perpetuity” - the engine license is terminable if you breach.