This is from the 80's when bike shoe makers provided specific/proprietary designed cleats for the shoes you bought, they came as standard equipment so your shoes fit properly on all bona fide road/track bike quill or caged pedals. This one looks familiar, maybe from Marresi road shoe? Anyhow you have a real mystery there that fits a certain make of vintage road bike shoe not made anymore, to find it you need luck and to search ebay vintage bike shoes. If you share this image with the infamous YELLOW JERSEY bike shop in Wisconson, chances are Andrew will ID this cleat right away, so you can search for the said mystery shoe