It's technically possible to do a card present transaction without the internet working. I haven't seen this happen in practice on ground, but it's actually very common on airplanes, especially on Ryanair. You can pay for everything on-board with a credit card, using a physical terminal, and I can assure you that they don't have satellite internet. They just post the transactions when the plane lands.

But I am somewhat curious as to why nobody in my experience has implemented this on ground. Because if the customer pays with an actual credit card, the risk that the transaction won't go through when the internet comes back up is near-0, provided the card is valid. It is theoretically (and I assume practically too, given that every credit card agreement I've ever signed--and it's a lot of agreements, considering I was churning a lot for airline points--specifically outlined extra fees for "overcharging" your account) possible to overcharge the account this way (i.e. the transaction would still go through even if it'd blast past your credit limit, up to some limit though, probably)