You can tell which cars are Gulf spec because they have all required labels (warning labels on mirrors etc) in Arabic instead of English.

If the warning lables are in English or some other language, then it's a grey market import.

If a car was sold in the gulf, it's possible that the air conditioning is better than the European version, but it could be exactly the same. Car manufacturers try to standardise as much as possible.

That dealer in the US isn't going to change all the warning labels from English to Arabic because it will be too expensive. Everyone will know it's a grey market import.