....they are connected to the internet? Either via cellular data, local WiFi, or a lan cable.

Technically there is a method of taking credit card payments (not debit, credit only) while temporarily offline, but the merchant doesn't receive any funds and no transaction is posted to the credit card holder until those offline transactions are submitted to the merchants credit card processing service, processed, and approved.

This has more risk involved than online immediately validated transactions because it can't verify the funds are actually available at the time of the transaction so very few merchants or card processors will allow it.

The prevalence of chip+pin security has pushed all the manual card entry methods out the door in the name of security. Credit Card issuers/processors don't like dealing with fraud cases, so they don't allow customers to use their cards in ways that promote fraud.