Yes, all transactions require the internet. For a transaction to be confirmed it needs to hit the blockchain. So this requirement isn't restricted to retail transactions, it applies to EVERY transaction.
It's absolutely a restriction for Bitcoin's survival and expansion. But there is much incentive to get the internet to those who don't have it already, and these efforts will in turn help Bitcoin's adoption.
There are still many parts of the world, including stores, taxis, but also people with smartphones, that do not have Internet. It is doubtful that even in the long-term future everyone is going to have internet on their smartphone. So how is bitcoin going to work for retail transactions? Imagine a store without public wifi. Can transactions be processed if only the vendor has Wifi?
Credit cards can work on either a phone line or internet, so it would be ubiquitous as opposed to bitcoin which cannot work on a phone line?