I think, personally, that the eight basic political categories will hide a huge variety … when the political setup of an entire planet is boiled down to a single word, it's going to miss a lot of the subtleties.
But from a historical point of view, a feudal society is at its core an oath-based society, where a ruler rewards followers with some form of property - sometimes loot, sometimes land, sometimes a bit of both - who in return owe service (usually military) to the ruler. Everything else, though, is up for grabs. Western European feudal societies (which didn't think of themselves as "feudal" - the term was coined by 19th-century historians) tended to be based around inheritance, usually but not always through primogeniture, where the oldest (usually but not always male) child inherited everything; but this is not necessary. You could have kings chosen by election or acclaim; kings for life, or for set periods, or until de-selected by one means or another. Nobles could be similarly selected and deselected. And although human beings might tend towards alpha-male hierarchies, there's no requirement for non-human cultures to do so (or even human cultures, long cut off from the rest of the species).
Chuck some religion(s) into the mix, and a planet where some areas are (perhaps enormously) more sophisticated/technologically advanced/connected to the Co-operative than others, and you have a huge range of possibilities. Great chunks of any given planet may not think of themselves as being part of a single planetary culture, and may not recognise any exterior definition. Even supposedly feudal Europe had hundreds of self-ruling towns, communes and religious communities, all with their own rights and privileges and ideas as to who - if anyone - they owed allegiance to, and for what.