"They do not read Chinese books."
汉语refers to the mandarin spoken language. 中文is the written language. Therefore it should be 他们不会读中文书
I just got it wrong for using 她们, which is ridiculous - can we please get this fixed, Duolingo?
在 means the action is continuous. In Chinese, it is not allowed to use 在 on an inexistent action (do not read). The negation on a continuous action is on the whole thing, so 他们不是在看汉语书 or 他们没在看汉语书.
Thanks for the explanation regarding negations! It does make sense that a non-existing activity is not continuous! "They read books" could describe a hobby, hence continuous. From the tips, it is not clear whether 在 can or cannot be used with negating continuous activities...