OK, I may not know much, but I know that if you dont adjust the pins, which wasn't mentioned in question,that gap will get bigger as you move the sight ring in. The yardages will be off, but the gap wil appear bigger.

If you are adjusting the pins to where the yardages stay the same, you will have to then draw the pins closer to make the yardages equal again. Same yardages=smaller pin gap when sight ring is closer.