So maybe I'm not understanding what you mean by generating narratives after all.
I can easily imagine, say, melee combat rules that aren't based on resources. You get your basic attack (and defend?) rolls, with special abilities that can be used either situationally (e.g. flanking) or with risk:reward (attack with advantage, but your opponents also get to attack you with advantage).
Then add in spellcasting like Shadowdark, where you don't have spell slots or mana points, but if you fail a roll you lose the spell for the day. If that's too "resource-adjacent" for you, then maybe the rule is that if you fail the roll you roll instead on a mishap table.
Instead of HP, you use defense rolls to mitigate successful attacks. Depending on how they compare, you either avoid the attack completely, or you are Wounded (disadvantage on all rolls?), or Downed.
There, no resources to track. How is that just a "prompt engine with randomizers for generating narratives" in a way that is meaningfully different than a resource-driven game? It seems to me the only substantive change is that the game becomes one of optimizing decisions in the immediate present, instead of a game of conserving resources for unknown future challenges.