Why caliber alone does not determine turret-ring size

How much larger would the turret ring be for twin 9.2-inch guns than for twin 8-inch guns?

Probably very little by caliber alone; the breech and mounting arrangement would control much of the actual diameter.

Twin 8-inch and twin 9.2-inch turrets need not have very different ring diameters. The guns are close enough in size for the mounting arrangement to matter more than the change in bore alone. Breech design is singled out as another influence on the space required. The German arrangement is criticized for taking more room than the British, American, or Italian alternatives.