Presumably, they use an off-line transaction. The reason your credit card has raised numbers is that, in the old days, before ubiquitous data connections, a card transactions used a machine like this
to transfer an imprint of your card details onto a form, using carbon paper. You would then sign the form and the merchant would send it off to the bank to get paid. It wasn't possible to verify in advance that you had enough money in your account but the deal was that the bank would honour the transaction and then come after you with a big stick. The point of my mentioning this is that, although we're now very used to the idea that the merchant talks to your bank while you make a card transaction, this wasn't the case even 20 years ago.
Today, it's still possible to make a card transaction without verifying in advance that the card has sufficient funds, so that you can still buy stuff on your card even if the merchant's phone line or internet is broken. In fact, the last-case fall-back is to go back to the swipe machines and carbon paper.