Since you mentioned plastic cards
It seems the phone in this case is just being used to display a code. So there's actually nothing about this system that needs the customer to have anything electronic - it seems it would work just as well with the QR code printed on a plastic card.
I'm assuming here that the code is constant for a given account. Others seem to think it's a generated unique code for the transaction. The latter would be more secure, but the description in the article doesn't really make it clear which is actually the case.