This is clever, and I want to spend some more time thinking about it. In a sense, I think this is basically saying that you can put the standard SAT-style analogy questions ("Lumen : Brightness = Inches : Length") in a square, and that most crossword clues could be represented as weird SAT analogies. Or maybe I'm stretching the analogy.
But I think that the "Diagonal" that the author suggests for the connection between "Donkey" and "Elephant" and "Party" isn't quite correct. The key is that both the Donkey and the Elephant are a "Party Animal." You can't ignore the "Animal" part, it describes them: they are each the animal that represents their party, the "party animal."
I'm not sure the correct way to represent this in "Square Theory," but it's not just linking "Party" to the animal in question.
But I think that the "Diagonal" that the author suggests for the connection between "Donkey" and "Elephant" and "Party" isn't quite correct. The key is that both the Donkey and the Elephant are a "Party Animal." You can't ignore the "Animal" part, it describes them: they are each the animal that represents their party, the "party animal."
I'm not sure the correct way to represent this in "Square Theory," but it's not just linking "Party" to the animal in question.