The accepted contractions are automatically generated and in a few cases it doesn't work. Apparently they can't change it though. You should report your answer that wasn't accepted.
"Will you have dinner" is right i would say but they still have not fixed ''Will you dine or Will you be dinning."
"Dining", not "dinning".
Also, "dine/dining" is extremely formal and wouldn't be used in ordinary households. You might hear it in a restaurant from the head waiter, or in a mansion in New York City.
How "Will you be dining?" be considered wrong when there is no context to judge by?
Will you dine? or Will you be dining? aren't quite right because "to dine" can be used for any time you eat, and the Russian is specifically talking about dinner/supper.
as a native english speaker I would almost never use the word "dine". It feels very formal in a way I would never be with anyone I can think of. I think the only people I ever hear use the word "dine" are waiters.
There are on-going discussions/arguments in English as to when supper or dinner occurs. It depends on region in the US. From my region, supper is an evening meal, as is "dinner" - except on Sunday, where "Sunday dinner" happens in the early afternoon.
Except it's not in question form in English, which is verb-subject, "Will you have dinner? (With compound verbs, the question form is auxiliary-subject-participle.)
Is a Russian way of inviting someone to have dinner with you - to stay for dinner, or join you for dinner if you're out in public? (The implication being that you will provide the meal.)