I just returned from Kidani Village today. I spoke to one of the bartenders at the Magi Pool Bar.
He told me about the private dining options. He showed me a a decent menu for adults and a kids menu. He said if you want ot order food just pick up this phone, order your food and take this number to your seat so your deliver person can find you.
My daughter ordered a kids pizza that came with carrot sticks, a fruit cup, and chocolate cake. The food was delivered to us in under 30 minutes.
As I mentioned there were adult options as well. Some were very expensive; like pork ribs for $20.99 which included a side and dessert I believe.
Additionally, there is breakfast food located in the gift shop. Granted it's not hot food like eggs and bacon, but there are cold cereals, and breads to choose from. There's also coffee, tea, and soda for refillable mugs.
I have photos of all this, but I can't post yet since photobucket is doing site maintenance right now.