Sounds like the score reels are not resetting correctly. I can't tell from the video if they are all zero or not. Maybe manually set the score on each player to NOT be zero and see if they all reset. The other item that needs to be reset is any BONUS relay must be decremented and then advance to the first bonus (1000).

The score motor is waiting for the reset cycle to finish - the Score reels and Bonus relay are a start. You need to check the schematics.

Other items to look at - Game Over Relay and the reset relay itself.