I'd say it would be incredibly rare for any native English speaker to say "what is the dinner" because it implies there is a type of dinner you can have. You can easily say "what is the fish" because there are different types of fish (cod, herring etc) but because there is no dinner "type" the question should always be "what is FOR dinner". Also, I disagree with "What is/that/dinner" - none of those question options work grammatically in English.
I think they should work grammatically, but the collocation "FOR dinner" is so common that nothing else sounds right.
As always, it's possible to construct a scenario that would make them work: let's say we're having TV-dinners; I chose to have the beef dinner (with extra MSG!). I turn to you and see that you're holding something else, more healthy perhaps, so I say "what's that dinner?" or "what's your dinner?"
Now, don't get me wrong: this is very unusual. I just don't think it's ungrammatical outright. But I am totally on board with the fact that "what is FOR dinner", as you mentioned, is the normal way of saying it and all other ways are highly marked (i.e. exceptional)
"The evening meal" would be a good translation, I think, though Duolingo does not accept it. It is accurate, quite common in English if a little formal, but neatly sidesteps the English class-ridden distinctions between "tea", "dinner" and "supper", which describe the same meal to different social groups...