My take is that if there is software, there is a computer, so my first reaction to the question was “We are trying to disrupt the shopping experience here, why list all the traditional ways when we’re talking about e-commerce?”
But even leaving out the obvious desktops, laptops, tables and smartphones, a dumbphone would definitely count and in the developing world where a lot of bandwidth is not readily available, both SMS and even WAP based solutions are used quite extensively.
SMS payments are also often available for small transactions such as unlocking a single paywalled article (however that would require a computer to deliver the bought item). A code sent via SMS could also probably work for some other types of transaction though.
Then, there are the self-service POS. I wouldn’t consider all vending machines to be e-commerce although one might argue that anywhere a credit/debit card is supported there is already enough software involved.
Also self-service ordering in a restaurant wouldn’t count as e-commerce for me even if the entire service chain was automated as the customer must be physically present at the same place as the goods are.
However, ticket vending machines which are connected e.g. to a railway reservation system meet my criteria for an e-commerce application.
Another such channel could be ATMs where you can add airtime to a prepaid mobile phone.
The latter two types typically run Windows though, so I’m honestly not sure that they count as non-“computers”.
And finally, if Google get their way, we will perhaps soon be chatting with bots on the phone to order stuff remotely, no need to touch a computer.