Your chip was made by Hunt & Co. beginning in the mid or late 1920s.

Hunt only sold chips with that embossed double ring design with a star in the center. As you implied, the star was part of that double ring or circle mold design.

As a ChipGuide Admin, if I processed this chip as a submission. I would probably categorize it as a variant of the "Circle" mold.

My thinking is that someone trying to look it up using the ChipGuide Mold query, would see it as being closest to that mold category. Other mold categories for it could be "Plain (engraved)" or "Raised Circle", but I don't think that they are as close.