The diagram actually shows how this DOES NOT reduce play in the wheel, but is just a brake. If the steering chain/cable assembly is loose causing play in the steering, once this brake is tightened, there will still be play in the system. As you can see, the brake clamps around the shaft of the steering wheel just making it harder to turn. If you tighten it enough, the wheel will be locked.
Think of it this way: You have an old car that has lots of play in the steering; you cant hold a straight line and it likes to follow any cracks in the road and wander from side to side. Now, somehow, you are able to solidly lock the steering wheel in a position straight ahead. But, the car still wanders along the road from side to side and won't go in a straight line because of the play in the steering system.
This is the same as applying the steering brake on the Edson wheel. Even though the wheel is locked, the system play is still there.
Catalina 38, Hull #112
Grosse Ile, Michigan