Fair enough man. Well to keep Superman stuck in Metropolis, an easy answer is that Brainiac attempts to bottle the city at the start of the game, but Superman/Lex interrupts the process which leaves the process half finished. Metropolis is enveloped by a force field that surrounds the city which Superman can’t punch through. There that keeps him contained inside Metropolis.
Personally I’m pretty fine with “it’s a video game so they have to set the map limits somewhere”, but that’s an “in-lore reason” for you. Future games could also simply use the reason of the villains threatening to go on rampages and kill civilians if Supes tries to leave so he refuses to leave until everyone is locked up.