I found some very old discussions of Emirati cuisine, but figured it would better to create a new discussion. A new place has popped up in Floral Park offering some interesting Emirati dishes.
Shank House Restaurant Dubai Cuisine
259-07 Hillside Avenue, Floral Park
I have tried the mandi, a dish of rice and meat similar to biryani but cooked here in the Emirati/Saudi way, as well as a wonderful salona, a meat stew which uses the powder of dried fruits for its sourness.
I will link my full post here if you want to see more. A couple attached photos have the full menu.