'They are eating despite having no hunger', is this not correct?
Well, your sentence is grammatical. But it sounds like something a foreigner would say. English prefers "they are hungry" to "they have hunger" and "being hungry" to "having hunger".
"They are eating despite they are not hungry." What is wrong with this sentence?
How about: They are eating, although they are not hungry. ?
Sure, that's accepted, too.