Also it turns out there is a mechanism that Apple could use for loyalty card data transmission.
https://www.paypass.com/PP_Imp_Guides/IMCR_Manual.pdf page 10 talks about data storage features on the "card" itself that could be used for that purpose. The specific data format would depend on the retailer of course. If there is some sort of NFC related API or at least something to store this data, it's definitely not public.