probably only to the extent that any hierarchical, oppressive, obedience-demanding institution could be considered a government. clearly different folks have different ideas about what constitutes government (or a state).
A kleptocracy is just rule of one or more thieves. In a way it doesn't describe a government, but in other ways it can. It's more commonly used to describe a government that's entirely corrupt though. For example, Russia is commonly referred to as a kleptocracy.The mafia did or does outright have sovereign control over certain areas and it's kind of a confederation type of thing they have going on. Depends on which one, I guess. The boss is elected and has an underboss and other advisors below him. Then there's provincial representatives for whichever "family" that claims whichever area. The boss isn't necessarily the boss for long if he's determined to be incompetent or something. When that occurs, a new one is elected or the old boss is overthrown. To join, one must be of a certain group and do certain things to prove themselves. The main goal of the mafia is financial and territorial gain. Maybe not exactly a kleptocracy, but close enough. The way the mafia is structured and functions is similar to a government.