Like for example "fire archon" means the same thing as "archon of fire"? Right? Is there any instance where this might be false?
So, what you're talking about is an adjunct noun or attributive noun, where one noun is used to indicate attributes of another noun. This isn't precisely the same as using it as an adjective, because if it were an adjective, "X Y" would mean "Y that is X" - "red shirt"/"shirt that is red".
What you're doing is working out the fuller phrase that corresponds to the simple noun phrase, and one of those expansion would mean "of". However, there are some that mean "from" or "for", or even "by". For example, "Melton Mowbray Pork Pie" is a type of pork pie that comes from Melton Mowbray (which is a town in Leicestershire, England), and a "trouser press" is a press for trousers. An "Agatha Christie book" is a book by Agatha Christie.
There are other prepositions that can be implied as well. I wouldn't even say I was 100% that it would always be a preposition.
I'm not even sure if I agree that a "fire archon" is "an archon of fire".
I have to admit, I didn't know what it was so I looked it up. So it is a fictitious creature that from appearances seems to be composed of fire. So "Fire Archon" is a common-noun (assuming there are many of them), and a fairly apt one too, not dissimilar from the common noun "snowman" which is a "man" made of snow. This is not a "rule" of English though - this is just a naming convention, of which there are many.
To say that a "Fire Archon" is an archon (a "ruler" or "leader" as in "Archangel", a chief angel, or "Archbishop", the chief bishop) of fire would mean that it rules fire, not necessarily that it is a ruler made of fire. Maybe it is both, I don't know. My point is that any words you can find that do seem to follow the pattern of your example do not necessarily mean the same thing. A "man of honour" does not mean he is made of honour like the "man of snow" is made of snow.
Consider a "pond-dweller", which might be used to denote any creature that lives in a pond, for example, a frog. It is neither a common noun (frog) nor a proper noun (Kermit, perhaps?), but an attributive noun. It is a name for an attribute of a frog. Also, this does not quite work the way your example does - you could speak of frogs in general and say "the frog is a dweller of ponds" (plural) but you would not say of a particular frog "Kermit the frog is a dweller of a pond". It just doesn't scan.