This circuit seems pretty timing sensitive - there's kind of a race condition in it.
Bowling Queen 50pt relay (resized).jpg
When a rollover switch closes for the first time (use the Top Left RO in this example), a pulse goes through the make/break switch on the #1 trip relay then through the #1 trip relay coil and the series P relay coil. What should happen is that the P relay should fire and close the P relay switch in the red box to fire the K/50 point relay.
What happens at essentially the same time though is that the #1 trip relay fires, which throws the make/break switch to the other side and connects the rollover switch to the J/5 point relay. When that make/break switch flips power to the P relay is cut because the P relay doesn't have a lock in circuit to hold it.
What should happen is that the P relay switch in the red box should fire the K/50 point relay which should open the normally closed K/50 point relay switch and prevent the J/5 point relay from firing (or disconnect it if it has fired).
What may be happening is that the P relay switch in the red box is gapped wide enough that the #1 make/break switch cuts power to the P relay before the switch in the red box can reliably fire the K/50 point relay. So the J/5 point relay fires instead because that normally closed K/5 point relay switch never opens. Or that P relay switch might just be dirty.