The only word I can think of is "extended family meal" or "friend meals", but since this is a common activity I think there should be a more general word. Most of the time it is home-cooked, and sometimes it's for a special event meaningful only to those people.
In the Vietnamese language we don't have a generic word. We just say "eat at X's home."
As an unrelated information, "family meal" seems like "nuclear family meal" to me, and in restaurant terminology, it means "a group meal that a restaurant serves its staff outside of peak business hours", aka staff meal.
Best Answer
Large gatherings are actually not so common. Normally they would be associated with particular events. Christmas and (in North America) Thanksgiving are two times when extended families have a meal together. You would call this "Christmas Dinner"
There would nearly always be a reason for a gathering. Whether it is Christmas, "Sunday gravy" or in my family "Nan's birthday". In your picture it is Thanksgiving.
One term you might find useful is "Dinner party". This suggests a fairly small number of friends (or extended family members) coming to eat dinner at someone's home in the evening. At a dinner party home-cooked food is normally served. It suggests a certain attempt at sophistication (the host might try to cook something special) and children might not be present. The term "Lunch party" is also possible.
An alternative would be to say "Eat at ***'s" For example:
(Stephenson is a family surname)