Words have meaning. It seems perfectly obvious to me that the Caliph leads the Caliphate and that the caliphate is the multi-national collection of islamic states. In general terms, the Caliph is an emperor, which makes restoring the caliphate an imperial project, and radical islam, which wants to restore the caliphate, an imperialist venture.
Then the world turns upside down.
The putatively anti-imperialist forces in the west on the left tend to be the softest when it comes to radical islam. Bill Maher has made left wing softness on radical islam a major theme of his career. But even Maher doesn't look at radical islam in terms of empire. For him, his opposition is part and parcel of his deep commitment to atheism. To him radical Islam is just religion on steroids.
Finding anti-imperial critiques of radical islam arising from the left is tough going. This provides an opportunity to call out the left and for a new left to arise that is authentically anti-imperialist no matter where imperialism arises.