Personally i think using "Arab" here is wrong. It should be "Arabian" as you answered.
Arabic means the language اللغة العربية
Arabian is a more formal synonym of Arab when talking about geographical places.
You cannot say "Arabic coffee". Arabic means the language (or related to the language) of the Arabs. "Arabic coffee" would mean "coffee related to the Arabic language"
Interesting that the english language distinguish between those both adjectives Arabian and Arabic. In swedish for example it is 'arabisk' in all cases.
I know, in French too we say arabe in all cases. But different languages have different ways of working I guess haha