Yes, there is no a "to be" verb. This example isn't an exception, when you make an adjective definite (adding al in front) you are making it part of the noun "Dou Happy" (in english it might be better to say Dou (the) Happy) vs without the al you would be saying "Dou is happy"
Both are the same in Arabic..
When the two words are found alone, a copula (is) is implied : Duo (is) Kareem
When saying, for example, "Innahu Duo Kareem إنَّه دوو كريم ", you certainly only mean : "He is a generous Duo " because you've already put the verb-like word (inna إنّ).
Naturally, we always consider this 2-word structure as " Duo is Kareem ". This is the natural way Arabs speak.
I'm just a beginner, but I've read that the third person pronoun is sometimes inserted in MSA nominal sentences, which the following link calls "equative": http://www.llf.cnrs.fr/sites/llf.cnrs.fr/files/evenements/colloques/DG_copula.pdf The reason this interests me: Modern Hebrew can have a zero copula in some circumstances, while in other circumstances uses the third person pronoun, הוא, and also זה
It would work that way in Farsi or something, but in Arabic, the sound /v/ doesn't exist, and in Standard Arabic waaw represents one of two sounds: /w/, a consonant, or /uː/, a long vowel. If you see two in a row, that means one is one and the other is the other. In this case, the first is the consonant, and the second is the vowel, so you pronounce it "duwuu."
But isn't "Duo" "Duo Lingo"? You must be an artificial intelligence (not very intelligent) because a normal human being would not be that rigid. Just as you rejected "strange" in preference to "weird". Well, although I know the meaning of "weird", it is not part of my active vocabulary, and I feel it is somewhat judgmental--negatively. I think, people over sixty-five are less likely to use "weird" than those younger. I cannot see myself telling someone, "your husband is weird"; I could see my daughter do so. And I would claim that someone who is weird, is definitely strange. Every time I add a comment to a translation, even a question mark, you mark me wrong.
You cannot add comments to the translations or your answer will be marked incorrect. A computer "looks at" the answers and is programed to accept what it is coded to accept as correct. Extra words can only be "read" as an incorrect response. Also, Duolingo staff and course creators do not, nor can they, read the millions of comments made by people all over the world taking all the classes that they offer. These discussions are for you to ask questions of your follow students about something you don't understand regarding the sentence with which that particular discussion is associated.