The Montevideo Convention is certainly a very good place to start and, as be said before that requires a movement to have
- A ) a permanent population;
- B ) a defined territory;
- C ) government;
- and D ) capacity to enter into relations with the other states.
Now, they have A) for sure. There's a group of people who live in cities like Mosul and they are permanent. Some of the population are transitory (leaving and going), maybe even a majority but there is a large group who are totally permanent.
B) is a little less clear. ISIL has continued to make claims about the illegitimacy of existing boarders in the middle east but that's not to say that ISIL does not hold a defined territory. They certainly don't recognise most of these boarders as anything more that front lines but they're lines nonetheless. I would argue that given their clearly defined Wilayahs (regions/areas/prefectures) they have a defined territory so fulfil B but I recognise that that's unclear.
They certainly have a government so C is no problem.
D ) is unclear. I would argue that to have the capacity to enter into negotiations is unconnected to having the will to enter into negotiations. I reject the idea of pouring hot coffee on my arm but I do still have the capacity to do so.
A counter argument might be that they don't have the capacity to enter in negotiations because they have no state counterparts for these negotiations. I don't think this is accurate though since they appear to have been negotiating with Jordan, Japan for the release of Kenji Goto and Muath Al-Kaseasbeh. So their capacity to enter into those negotiations has been demonstrated in my opinion.
The Montevideo Convention is ugly subjective and there are other standards that you might want to use but it's as good as all the rest. I accept B is a little shaky because of their rejection of national boundaries but I think it's worth think de facto rather than de libre on this.