No, I answered literally "He sleeps with open eyes" and it was accepted. However, the suggested translation "He is sleeping with his eyes wide open" seems more natural to me. I'm no native speaker, though.
It depends whether you want to say that he usually sleeps like this (then you go with present simple) or that he is sleeping like this at this moment (then you go with present continious). Both are perfectly natural.
I wrote "He sleeps with his eyes open" without the "wide" part and it marked me wrong. My son does sleep with his eyes partially open and we've said that in English. I don't see the "wide" part there in German to be marked off.