I think it should definitely be "scrivo i libri". There seems to be no consistency in this course concerning use of the article with the noun. When in doubt, use the article. Also the word list at the end of each lesson should include the article so the student can learn the gender of the noun. You can't always depend on the vowel ending. There are exceptions to the a/o fem/mas rule and some end in e which can be either.
He's talking about what he does "I write books". You answer the question "What do you do (what's your profession?)" by saying "I write the books.