The impetus to get retailers to start using the chip was "Liability shift". The payment networks gradually changed the rules (I think in the US pay-at-pump gasoline purchases were last to get this, while big retail stores were earlier) so that the liability if a transaction is latterly discovered to be fraudulent is with the retailer who accepted the dodgy transaction, not the payment network if the retailer didn't use the chip.
But I imagine if you're a little store in the country, maybe you do six card transactions per day, almost all of them with customers you know personally who just find the card more convenient, liability shift isn't a huge worry for you, while the cost of a new payment terminal is a significant issue.
The actual payment infrastructure doesn't care about any of this. Those old impression machines? Mag stripe? Put the card in manually? Tap your iPhone? In all cases the actual transaction which moves money, "Settlement", just needs the account number to take money from and amount to transfer. These different methods have different "Authorization" behaviour but Authorization is about mitigating risk for the retailer, and the bank, and only very tangentially intended to have any benefit for you to customer, it doesn't move money, and it isn't mandatory.