Here is the maximum extent of the Ottoman Empire (circa 1590):
Here is the propagation of Arabic culture, prior to the modern era:
As you can see there is quite an overlap.
However, while these territories were considered Arabic during the time of the Caliphates and are generally considered Arabic in the modern post-Ottoman era - for the Ottoman Empire they were not considered Arabic territories or a singular Arab empire; despite retaining the same religion, language and culture of the earlier Caliphate era.
So why was the Ottoman empire not seen as an Arabic empire?