> Used as an intensifier with statements or terms that are in fact meant figuratively and not word for word as stated

That is not the same as the meaning of “figuratively”!

“‘Literally’ is used with statements that are meant figuratively” does not mean the same thing as “‘Literally’ means ‘figuratively’”.

> "it hurts so bad I’m intensely dying" would be wrong too

Indeed, because “intensely” is not an intensifier. In your example, “intensely” modifies “dying”, whereas “literally” modifies the tone of your utterance.

For an example of another intensifier: “it hurts so bad I’m fucking dying” would work.

Nobody would claim that “fucking” means the same thing as “figuratively” in this sentence, even though the sentence is itself figurative.