It's because there are white label credit cards that are extremely easy to setup if you're a business and they're so profitable. Not only does the store get a sale upfront which a customer might not have been able to afford without it, they get additional revenue when folks are slow to repay their bill.
Do you know if these first part transactions also bypass Visa/MC and interchange? It seems like they should have it so the affiliated merchant can just send the charges over to the issuer directly and bypass everyone else.