What is referred to as "Islamic" culture did not come from Arabia/modern day gulf countries. It came from Iraq, the Levant, Egypt and North Africa. The Caliphates' capitals were based in Damascus, Baghdad, Egypt or south of Spain. These were diverse societies and "Islamic" progress was diverse by people from different religions and races.
Also, the Ottomans never occupied Arabia/the Gulf. They stopped at the Levant. Because there was simply nothing to occupy in an empty desert.
You're confusing Arabia, Levant, Iraq, Egypt and North Africa. Arabia has a very distinct culture and different languages & history.
The Levant, Iraq, Egypt and North Africa are far far from "still a desert with no social, architectural or technological progress". They don't even have oil, apart from Iraq.