In the roleplay, the Dream SMP is presented as a ceremonial monarchy, during the L'Manberg revolution, a L'Manberg revolutionary named Eret betrayed L'Manberg and was coronated as the king of the SMP yet it was very clear, Dream was still in charge. Later, during the Manbergia-Pogtopian War, Eret abdicated the throne to fight on Pogtopia's side and then Dream coronated George as the king. Later in the series, we find out that Dream has stolen items from everyone it attempt to control everyone. Using this information we can determine the Dream SMP is:
A ceremonial monarchy that does not actually follow any sort of line of succession, instead the monarch is chosen by the true leader. It is also a pseudo-totalitarian state where the leader uses personal property to control his subjects.
In the roleplay, most people on the server have their own personal property that they can control. There is also the Community House, a state-owned building that provides resources for anyone that wants to come by, this presents the Dream SMP as a sort of socialist economy where resources are state-own until you realize that a free market exists within the SMP and members of the SMP often trade with each other. So it can be described as a Market Socialist economy? Players on the Dream SMP often set up buisnesses however the products they produce are made from their labour.
So I guess you can say that the Dream SMP functions under a dual economy with one part of the economy being a market-based worker co-operative and another part of the economy being a state capitalist economy.