There never was a "Great Caliphate" though: some really great times for the Caliphs, their families, and their courtiers, mind you, but really atrocious times for their subjects, their slaves, or their neighbors. (Reminds me of Mel Brooks' famous line as King Louis XIV in History of the World, Part I as he fondles some bystander's breasts - "It's great to be the King!".
Like many other figments of somebody's fevered brain, that period of history is best left to the musty graveyards where it ended.
I don't see that the article claims that there was; it seems to describe the "Great Caliphate as a goal for the future:
The Third Jihad now had a base of operations and the oil wealth to support its grand design or what they call the Great Caliphate. . . What this design calls for is the replacement of all secular leadership in any country with Muslim majorities. This would include, Egypt, Turkey, Pakistan, Indonesia, all the Emirates, Sudan, Tunisia, Libya, Algeria, Morocco, Yemen, Syria, Lebanon, Jordan and finally what they call the occupied territory Israel.