The word has developed conflicting applications over time, but at it's core, it always means "without government." Interpreting it as a form of government just doesn't work.
The name is clearly inherited from the original Elite's cold war-inspired government classification which was
also a security level classification. It has to be read somewhat in that context rather than in any of the more normal English meanings. And the wider
problems come from Elite Dangerous being the first game where government not being a strict match to security state actually matters.
That said, you have to really push the boundaries of the word to interpret a corporation, or a religion, or a prison colony as a form of
government either.
"Prison Colony" is in many respects actually rather less coherent than "Anarchy" in terms of being a faction government type. Settlements (or even entire systems) could certainly be prison colonies, but that should be either an
economy type or just a part of the settlement name, with the controlling government just whoever happens to be running the prison. What does it even mean if the Hodack Prison Colony faction takes over a new station? Are all the inhabitants instantly jailed? [1]
"Corporation" implies some form of recognition and incorporation
under a government - if one had its own ability to set laws, and fight wars and gain territory as part of its completely independent foreign policy, then it can only meaningfully be incorporated under
itself. And at that point it's basically just a standard dictatorship with maybe some vestigial corporate titles from before it declared independence.
Forms of govern
ance, sure - as social structures for organising activity all of these are plausible ones. But then anarchy (any type!) is most certainly also a social structure for organising activity.
"Nothing about Elite Dangerous minor factions makes any sense" is true but we're not playing Elite Dangerous for its realism anyway.
[1] No, because that would be the Lockdown faction
state.