On this game, I'm pretty sure that the game over relay is continuous duty, so the coil is energized the entire time the game is sitting in game over. If that is the case, I suspect that this additional coil was added to serve as a current-limiting resistor for the game over relay coil, so that coil would not run so hot.
It's an interesting idea, but the execution seems less than professional. As Spinal Tap would say, there's such a fine line between stupid and clever.
- TimMe