Two resistors are called for on the schematic on the Balls Played unit:
Super Score Balls Played unit (resized).jpg
They're in circuits for alternating relays, or relays that will be active for an extended period of time (as long as the Balls Played unit stays in one position). The resistors may be there to reduce the arcing across the Balls Played Unit snow shoes when the unit advances and the circuit to the active relay coil is broken. There's one on the 0-9 unit too apparently for the same reason.
You should be able to just solder the resistor back in place, possibly after checking its value first. The game will probably work without the resistors with the added risk of additional arcing.