The terminals can almost certainly be set up to work "offline"
Some of them can. It depends on the device, and whether the service provider for the card machine allows it I believe (so some of the cheaper ones used by smaller businesses etc. might not work offline).
The main downside of using one offline though is that the transaction isn't actually processed whilst the machine is offline. It is stored and processed once the device is back online. The clear downside here is that if a customer's card is declined for whatever reason, the merchant will only discover this when the customer is already long-gone.
easyJet took €3 from my Google Pay at 40,000ft
At least one flight I took this year with either Ryanair or EasyJet had in-flight WiFi - it could only be used to access the in-flight duty free menu and some advertising for the airline/destination, but nevertheless suggests they have internet access which could presumably be used for processing card transactions (these use very little bandwidth). If not, and they're using them offline, the risk of a card declining post-landing is presumably reduced by the fact that they can record which seat numbers order what, and then chase up any customers whose payment doesn't go through.