I think it makes a lot of sense if you look a little closer at the roots.
televidi = tele- (prefix for "long distance") + vidi (to see) = long distance seeing (i.e. watching television)
Which makes televidilo a long-distance-seeing tool, or in other words, the thing you use to watch television.
Dmikon already answered this. The TV set is just the TV - usually with built in speakers. For additional clarification see link.
Regarding the link (below), I'm old enough (or my dad was handy enough) to have grown up with a kit-built TV set with vacuum tubes that needed to warm up. One of the tubes was loose so sometimes I had to open it up to jiggle the loose tube. I recall we had a rock sitting on it to keep it in tight. I should ask my older sisters.
I have some trouble with that distinction too. To me, a TV is the thing that may be sitting in the living room that would allow me to watch stuff. And a TV SET is??? As opposed to the thing that I can use to watch TV?
Or is TV seen as the CONTENT that is shown on the TV? I.e., when I say I watch TV, I'm not sitting there watching the gadget, but I'm watching the program that's shown on it. Is that it?
Yes, "television" (no article) is all the programming and content, as well as the concept of sending these visions through airwaves, whereas "A television/a TV" (specified by Duolingo as a TV "set") is the unit or tool by which to watch TV. Growing up in a small town, we had an antenna (attached to the chimney outside our house) and/or "rabbit ears" (two small antennae attached to the TV itself) to help us tune in channels. Later, when we got cable with more than 13 channels, we had to get a small box that was attached and had a remote control so that we could access the other channels. I think those things would all be considered part of what made up the "set."