Of course, and it has been around for over a thousand years.
??? There is no need to defeat the idea, and there is no way you would know the "idea" was defeated, so there will be no global upheaval in "defeating" the idea.
Presumably you are not now talking about the "idea" but the physical "Islamic State". If so, it is on the verge of being defeated in Iraq and Syria. There will be small pockets left here and there (not just in Syria and Iraq) but it is not now a "state" and IMO will not be a state in the future.
The battle for the REAL Islam, eh? How is "real" Islam defined?
Rubbish. The so-called Islamic "State" is on its last legs. The idea of the Caliphate will live on, of course.