You could still fraud hit them in this circumstance, but they have some kind of info printed on your card with your name on it and how long you've been a member, and somewhere in the background, a phone# and address.
If one wanted to commit retail crime, easier to just take stuff and walk out without paying.
Might lose some payments to overdrafts or cancelled cards. But they lived with that with credit cards up until 2000ish.
Buy-on-board on Aircraft and trains take advantage of this.
Offline payments is baked into EMV payments. It can at least verify the PIN and that the card was valid at its last phone-home.
https://www.google.com/search?q=mastercard+emv+offline+payme...
Once, while waiting to check in for a British Airways flight from Manchester (UK), I noticed several large plastic boxes behind the check-in counters labelled "manual check-in".
Presumably someone at BA not only thought about but actually implemented a plan for how to check in passengers when (not if) all the check-in computers go down.