Personally I wouldn't recommend disassembling the relays yet as you will likely cause more problems for yourself if you aren't too experienced. (No offense intended).
I think the main clue here is that the sequence progresses when you remove the ball from the outhole. This implies that the ball is therefore not being kicked out, so work back from there. From the video, it looks like O is not locking once activated by the bonus unit. please follow Rolf's excellent advice!
Don't use a continuity checker on your DMM in EM games or you'll get false positives. Continuity mode will beep when the resistance measured is below a threshold (say 40 ohms). e.g. if you were to check continuity across the circled O contact it would beep if the contact is open OR closed because of the low resistance path through the transformer. Much better to measure the resistance across contacts - you should read close to zero ohms when contacts closed and infinite when open.