Diamond mentions two different political structures that the Mongols had. These structures changed over time. At first, the Mongols' society was a chiefdom. Later, as the Mongols were able to conquer an empire, their society turned into a state.
At the end of Chapter 13, Diamond states that the Mongols who conquered China were a chiefdom. At this time, they did have a centralized government, but it was less organized. It was not the sort of government that the Mongols later had when they had conquered China. At that point, they had a highly bureaucratized government wtih laws and judges, not a more informal system where issues of justice were decided more arbitrarily.
So, the Mongols had a chiefdom but then developed a state as they increased the size of their empire.