For me, "key", and "critical" merely say it's "important", but don't convey the sense that "out of the mess of connected concepts we're discussing, the one that is actually interacting with the thing we care about, or at least dominating the interactions with the thing we care about, is X".

"operative" is a bit better, but I think of it as referring to grammatical interactions, i.e. interactions at the level of language mechanics rather than semantics.