Unless I'm not reading your picture correctly, the "chunks of hoop" appear to be rotating in the wrong direction.
I looked into it, the hoop is rotating in the correct direction (clockwise) for the ground on the bottom and the hoop rolling to the right. Note that the vertical axis on the right-hand image crosses at x=0.6, so the hoop has rolled a decent distance to the right. Sorry about the confusing image.I tend to agree with your observation. There appears to be a small mistake in DaleSpam's original equation that has the ball rotating counter clockwise while translating from left to right in the positive x direction which does not agree with the contact point being at the bottom. This is a non fatal error that is easily corrected by reversing the sign of the y coordinates.