So the game tries to advance the stepper past position 5, but the stepper mechanically doesn't reach the 6th position. That indicates that the circuitry is working and that as you suspected something is mechanically binding the stepper. Since you've taken it apart it's possible that something wasn't put back quite right. No offense, it happens a lot.
That shouldn't be hard to sort out. With the power off try to take the stepper through all of its positions just by pushing in and releasing the solenoid plungers. The reset plunger ought to return the stepper to the starting position from all of the other positions. And the advance plunger should advance it to all positions reliably.
The photos Billc479 posted above show a couple of pins mounted to the stepper gear. These pins usually open and close switches at the limits of the stepper's motion. Check that those pins only open or close switches in the first and last positions. It's possible for example that a switch stack is mounted to the wrong side of the frame, or has the wrong number of spacers or something else that changed the relative positions of the switch and pin. It's also possible that the spring around the gear has too much tension. I think they typically need 3-4 turns if everything is clean and otherwise working.
This is the beauty of EM machines. You should be able to see this problem with the power off by just manipulating and experimenting with the stepper.