This is why. In the sidenote, it said that a sentence will use "Kein" if the subject has no article. Because it is just "Er", this makes it right to use "Kein", even if "He does not need a sleep" doesn't make sense. In almost all other circumstances, you would use nicht, except for if what your negating has an indefinate article.
He needs sleep. He does not need sleep. He does not need any sleep.
In this case, "sleep" is an abstract noun about the state of being asleep. It is not countable and does not take the indefinite article "a" or the definite article "the".
Note that "He is asleep" means that he is sleeping.
النفي في الألمانية بالصور التوضيحية مع أمثلة Die Negation, الكلمات الدالة على النفي Negationswörter, اعراب kein
If you translate it that way--which does capture the meaning/concept--you are transforming sleep (a noun: der Schlaf) into a verb, also "sleep" (schlafen).
So the more faithful translation to "He needn't sleep" would be "er braucht nicht zu schlafen", oder vielleicht "er braucht schlafen nicht."
Why is "He doesn't need a sleep" wrong? This is quite normal English though it means something slightly different. It's what you'd say to a baby sitter, for example.
If it's wrong, how do you say "He doesn't need a sleep."
To me "He does not need any sleep" suggests he never needs to sleep.
because "he doesn't need a sleep" is quite not normal English. He does not need any sleep doesn't sound to me as if he never needs sleep. "He never needs sleep" would fit, but, to answer your question, I don't think is possible. I think that would be "Er braucht einen Schlaf nicht" which I'm understood is not grammatically correct. -native English speaker
Well I'm a native speaker also. I've often said he/she doesn't need a sleep. I doubt I've ever said "he does not need any sleep." It's such a false statement. Everyone needs sleep but they may not need a sleep this afternoon. Perhaps it's an Americanism to say "he doesn't need any sleep." when you mean "he doesn't need a sleep."
I totally agree with CathyPinner. I and my associates would say "he does not need a sleep" when talking about a day time nap ( for any age). My initial thought on reading "he does not need any sleep", was that he was a robot, so never slept. I can accept that some people may use the latter phrase, but please Duolingo, include "a sleep" in your database too.