I have seen this as well maybe ~15 years ago at a hotel. Only it was SNES. It allowed you to select games from a menu (no cartridge). The controllers were hooked up into a box with a line dissipating into a wall. The controllers were different than normal SNES controllers. They were more like the SEGA controllers.

I don't know the mechanics of how it was arranged. They charged only an "access fee" and not per game, so perhaps it was a shared emulator / arcade style machine?

I remember this when I was younger as well and it was similar to how movies in hotels were you ordered through the tv and yes I believe you had an access fee in hours to play all the games available.