Your route and desktop are not an example of an internet connection. That's an intranet connection. I think that's what they mean -- for two devices to be connected on the internet there's always (at least) routers in between.
I can infer what they mean, it doesn't make it a correct statement. Maybe I'm being pedantic, but routers are devices too, and I have computers with multiple NICs that act as routers as well as servers. Intranet vs internet is an arbitrary distinction. If a "device" has an IP address that's reachable from "the internet" then it's on the internet, regardless.
The article's point is that to get information from Device A to Device B across the internet is never a straight link from Device A to Device B, there are always middlemen whose purpose it is just to forward the data along. There's always something between the end nodes.