Best case, the physical card, if they have one at all, will be a pre-paid gift card, not a card linked to your account. And the virtual card ... better than a physical card! ... will be a virtual gift card.
Worst case, they've had so much trouble getting companies to join the trainwreck that they're going to try to claim that the Chrome extension is, in effect, a virtual credit card in some sense that only the hardcore GAWbots will try to believe. And better than a physical card!