[hervature]

This is just the classic problem of mixing technical terms (like information) and using dictionary definitions. Personally, I believe they intend to say the same thing as you. What they are trying to say is that the lower the entropy, the more similar to a Dirac function. In their mind, this means you know exactly what the distribution is and hence "informative". But, as you point out, that just means you already know everything which is the exact opposite of information. In the context of Wordle, guessing a word with 0 entropy would be a wasted guess as you would have all the previous words remaining. That is, guessing a word that has already been guessed. How informative!