Rich resinous fragrance oil popular across the Gulf.
I would put Date-filled chocolates on the list for United Arab Emirates because it is the kind of thing that feels useful once you are home, not just another airport purchase. Look for a boxed version with a decent date on it, especially if you are buying it near the start of the trip rather than at the airport. The reason it works is that it gives you a quick reminder of the trip without needing to keep a fragile ornament safe forever.
This is exactly the sort of thing I like bringing back from United Arab Emirates: small enough to fit in a bag, but specific enough to remind you where you bought it. It is a good one because people can try it slowly at home, and it makes a nicer gift than a mug with a place name printed on it. It is also the kind of thing you can talk about when someone asks what you brought back, because there is usually a little story attached to where you found it.
Camel milk chocolate is worth adding because it feels like something you actually noticed while travelling through United Arab Emirates, rather than a generic souvenir. Look for a boxed version with a decent date on it, especially if you are buying it near the start of the trip rather than at the airport. The ideal version is modestly priced, not too bulky, and good enough that you would buy it again even without the holiday memory.