Crossroads Arabia reports on an article in Saudi newspaper al-Monitor by commentator, Bader al-Rashed. He is upset that apparently Daesh (aka ISIS/ISIL/IS) is distributing books in its territory of control by Muhammed ibn Wahhab, the founder of the Wahhabist movement that is the ruling ideology of the Saudi royal family since the 1740s. This would suggest that indeed Daesh is strongly Wahhabist in its fundamental orientation.
Al-Rashed in turn argues that no, they are not. Daesh are really Kharijites, a Muslim group from the early days of Islam that was neither Sunni nor Shi'i, and was strict in its views and was based mostly in what is now southern Iraq. They were famous for their intense takfirism, a practice of excommunicating people they viewed as not being proper Muslims. That would indeed seem to be something that Daesh likes to do. This is tied with the notion of apostasy, which is outlawed in 21 Muslim countries and punishable by death. I note that some interpreters of the Qur'an read the relevant passages as allowing for amputation or expulsion as alternatives, and certainly the last of these would be far more humane.
There are no self-declared Kharijites anywhere in the world now, and Daesh does not identify itself as such. The closest group, although more moderate than the old Kharijites, would be Ibadis, a group descended from a close relative of the Kharijites. They are dominant in Oman today and are neither Sunni nor Shi'i, actually seeming more moderate than most nations ruled by either of those.
In any case, it must be recognized that Daesh is drawing strongly on fundamental theology of the Saudis. The latter must oppose them because their declaraion of caliphate says they should rule Mecca, Medina, and al Quds, (Jerusalem). The king of Saudi Arabia;s proudest title is Protector of the Holy Cities, Mecca and Medina, with a successful Haj just completed. They do not claim to be caliphs, but do not wish to give up their rule of those cities, or that title.