It isn't the move to the center position.
He is finally used to getting his shots off with less athleticism and his timing has returned.
KG in his prime scored much the same way he does now. He had an array of turn arounds and pivot jumpers in the post, and he hit spot ups from mid range. He has never been a physical scorer...ever. Losing his freakish athleticism should not hinder his scoring.
The only reason it did in my opinion is that it took KG a couple of years to figure out his timing on all of his moves not being able to jump as high as he used to.
Keep in mind now that even with his reduced athleticism, we still have a (well) above average 7 footer in terms of athletic ability.
The only thing he cant do anymore is dunk over people and blow by defenders to catch lobs.
Everything else is still money.