I need a better term for internet-enabled or web-enabled that a non-technical person would understand includes their smartphone, tablet, laptop, desktop, smartTV, etc.
For one, I think @Dan D. is correct in saying that those terms by themselves should be pretty clear.
If you're looking for something that a very un-tech-savvy (surely that's a word) crowd could understand, I'd say swapping the word "enabled" with "connected" could work, even though it wouldn't be ideal.
Perhaps "always online"?
That'd be the only thing I can think of, short of changing it into a sentence like "devices that are connected to the internet" or @Kristoffer Nolgren's "with internet access".