At first I thought that the writer, Josephine Livingston, was saying that these were the main words --- like, the Old English word for sea is hronrad, "whale road." But no, if you look up "sea," that is Old English too. People normally said "sea," but sometimes if you were writing a poem you would make up these colorful alternatives. I think that's what she meant. It just took me a second reading.
At the end, she says this isn't possible in modern English. "We who speak contemporary English are so reliant on word order that we are no longer as able[...]. We just can’t do the same things with our vocabulary." She gives as an example that she wants to make a new kenning out of "poignant" and "solitude," but it won't work because today's readers would interpret "poignant solitude" as just an adjective modifying a noun, with no special poetical air. That's because she did it wrong.
At the beginning she defines a kenning as two nouns, but "poignant" isn't a noun, it's an adjective. She would need two nouns. And solitude, while a noun, is abstract. She would be better off with two concrete nouns, like the old kennings. The best I can come up with right now is "teardrop cloister." A more modern style, though, would be "cloister of tears."
I see no reason why you couldn't write a poem today with custom-made compound words like "whale-road" and "bone-house." The reader would have to rely on the context to figure out that you're using metaphors for the sea and the body, just like then. Maybe it would be a little more jarring these days. It sounds like back then that poets did it all the time. It was a meme. But modern poetry has this kind of wordplay here and there. And like I said, instead of doing it with compound words, they do it more by joining them with the word "of", like: "cloister of tears," "the road of the whales," "this house of bones." I could totally see any of those in modern poems.