Looks as much like a government as the one we support in Afghanistan. Stands to reason. ISIS may not govern their territory like a first word country, but they aren't a first world country. ISIS has only been in the governing business for several months. Ultimately they want a true calaphite. They want empire. It is clear they intend to govern under the law as they see it.
http://www.cnn.com/2014/09/18/world/meast/isis-syria-iraq-hierarchy/
http://time.com/3720063/isis-government-raqqa-mosul/
I absolutely think that ISIS's COG is the territory they occupy. Not only because they need it for legitimacy, but also to smuggle its oil across borders as a major source of funding for its operations.
ISIS is very much a rudimentary state. They have a system of government, a body of laws, an economy, and an army. The phrase 'we always fight the last war' comes to mind here, and it seems like the underlying assumption is that any ground operation would result in a protracted insurgency like OIF.
But our political rhetoric makes it more complicated to send land forces in to uproot them. We don't acknowledge ISIS as a sovereign state, so even if they are responsible for attacking a country there is no legal basis to violate Syria or Iraq's borders to uproot them. Syria and Iraq aren't asking us to come in and help, so ignoring the UN treaty to send in land forces would set a bad precedent here, even if bigger 'frienemies' like Russia and China don't intervene on some level to keep us out, let alone actual adversaries like Iran. That's aside from the aforementioned challenge of getting commitment from neighboring countries to sustain order post-war.
So like an alcoholic at his first AA meeting, the first step is admitting that we have a problem and what that problem is - there is a small nation governed by Islamic militants that wishes to expand its territory to conquer the entire Middle East and kill anyone who isn't Sunni Muslim in the process. Once we* can get past the political rhetoric of not calling them a 'state' or 'Islamic terrorists,' we can recognize them for what they are and shape an effective strategy to defeat them.
*we refers to political leadership as I'm quite certain some very smart and talented GOs have already weighed several options from all sorts of different angles.