Fate manages to combine an absence of hit points and narrative malleability and potentially a death spiral too.
Much as I like FATE (Core, specifically, but I don't think the version matters much in this case), I don't think it gets away from hit points in a truly meaningful sense. It elaborates them, sure, adding in "big" hit points and "little" hit points, but you still have a limited pool of
something that you can have ablated before you simply keel over.
When I think of a genuinely "non-hit-point" system I'm looking for a complete (or near complete) lack of any "life resource". There would need to be no pool of points or set of "levels" or collection of "traits" that, once exhausted, mean a character is "out of action". Rather, "out of action" happens stochastically, with the likelihood of it happening at any specific instant being strongly affected by in-game situation - particularly the condition(s) and hindrances affecting the character at the time.
All of which should not be interpreted to mean that I think "no-hit-points" is a neccessary or even inherently superior attribute in a roleplaying system.
I feel like this is very close to my position on the subject. Narrative malleability is something that I want to minimize as much as possible in a system, at least to the extent that it doesn't significantly increase the workload required to model anything. To me, the whole point of having a system is that it converts the objective reality of any action into a mathematical language that we can process and then spits back the objective reality of the outcome of that action.
At one time I think this was my (fairly fuzzily understood) desire, also. It seems odd to me, now, since I have learned so much more about how we actually view the world. Since the world is not really as we (think we) see it but, rather, every image of the world we have is an interpretation I find it much easier, these days, to view RPG systems in this light, also. Just as, in real life, we only actually sense sufficient cues from our environment to allow our brains to make a coherent model of what goes on around us which is good enough to let us survive, I now see RPG systems as merely providing sufficient "hooks" to allow us all to imagine the imaginary world as we wish without encountering too many clashes of understanding. As long as we all agree on whether the character is up and in the fight or collapsed on the floor (but with some chance of getting up again under some specific circumstances), it really doesn't matter if the specifics of injury, dishevelledness and consciousness are different from one person's vision to another. The idea that there is a unique, "objective" reality that is seen by all is a fallacy known as "naive realism"; I commend an investigation of it to you. It's real science, not some sort of fringe belief.