Is the Commonwealth of Man a classic dictatorship? Not necessarily.
We know a few things that are undisputed facts.
1:They're a Xenophobic and Fanatic Militarist. Not Authoritarian.
2:They have a Constitutional Elective Dictatorship
3: Their society is nationalistic. The Fleet and the Admiralty have unusually prominent roles in this society, wielding a great deal of influence in political circles.
Now here's my theory. Traditionally Commonwealths are separate semi-autonomous or autonomous political entities united by an autocrat or ceremonial autocrat who rules over them. British Commonwealth and the Polish–Lithuanian Commonwealth for examples
This makes me think that while on a geopolitical level they're one nation but actually are more federated on a more local level united by one military and ruler.