If these are truly illegitimate, there's only one way under the circumstances (and given Islam's union of church and state) to prove it--the other Muslims have to wipe them out, as they almost succeeded in doing with the original Kharijites.
Unfortunately what would seem likely to make them Not True Muslims isn't trivialities like enslaving and killing Christians--historically that's perfectly OK. And not ancient history, either. Where they go over the top is where they takfir-ize other Muslims at the flash of a CD.
So where do we fit into this picture?
Or, more accurately, where do American Muslims fit into this picture? Especially if the Daesh are, by default, legitimate interpreters of Islam?
We'll have to start distinguishing between religions one way or another...