So what are they? I'd like to know what to call their government.
Their political philosophy is called Juche. I've also heard them describe themselves as "the World's last socialism."
It is essentially aimed at creating a communist society, but with very strong Korean cultural and national characteristics, probably due to their bitter experiences of colonial exploitation. They seem to believe it is exportable, but needs to be modified to each national culture and its situation. It has an extreme emphasis on what we would call "isolationism" and "national self-reliance". Thus it aims at
1.Political independence [chaju]
2.Economic self-sustenance [charip]
3.Self-reliance in defense [chawi]
And its internal social principles are:
1.The people must have independence (chajusong) in thought and politics, economic self-sufficiency, and self-reliance in defense.
2.Policy must reflect the will and aspirations of the masses and employ them fully in revolution and construction.
3.Methods of revolution and construction must be suitable to the situation of the country.
4.The most important work of revolution and construction is molding people ideologically as communists and mobilizing them to constructive action.