I guess I think of Fortnite as a "custom" game engine since Epic owns both the game and the Unreal engine. So it matches the pattern, "FPSes are built on engine

I guess I think of Fortnite as a "custom" game engine since Epic owns both the game and the Unreal engine. So it matches the pattern, "FPSes are built on engines owned by the same entity that owns the game." But you could argue that since Unreal is commercially available Fortnite runs on a non-"custom" game engine. Depends on your definition.