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.
Rolemaster and its offshoots (MERP, HARP) mostly fit this bill. "Out of action" is dictated by conditions/debuffs, which are imposed by crit results.
RM also does have concussion hits, but these are only one component of the "health/life" system, and correspond to only one part of it: bruising and blood loss. Losing concussion hits can inflict penalties, including a dying condition, but it is by no means the only way to suffer those penalties, and as far as serious debilitation is concerned is not the main way that penalties/adverse conditions are acquired.
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.
In English-speaking philosophy, "naïve realism" is normally used as a label for the view that the external world is actually like the world of perception (eg it contains coloured, textured surfaces, sounds and smells, etc). The closest thing to a contemporary mainstream view, I think, would be that there is a single objective reality known by all, but that it does not contain those perceptual properties: scientific realism rather than naïve realism.
The position you are putting forward was held - at least from time-to-time - by Bertrand Russell, and also Moritz Schlick. It has its ancestry in 19th century neo-Kantianism, although the neo-Kantian label is probably more apposite for Schlick than Russell. It is a controversial view. In my own opinion it is refuted by AJ Ayer in his books The Origins of Pragmatism and The Central Questions of Philosophy. The basic gist of the refutation is this: ultimately, our only evidence for the truths of physics is that a certain lamp glowed red rather than yellow, or a certain dial turned this way rather than that way, or a certain image produced from a telescope had a dot in this place rather than that place. If none of that perceptual evidence has objective existence, then we have no rational basis for affirming the evidence on which our scientific view of the world depends.
That's not to say that the relationship between perceptual evidence and scientific reality is easy to explain: for instance, analysing
colour in a way that makes it true both that there is (say) a red lamp that I perceive, and that there is physical object (itself made up of colourless constituents with a lot of empty space between them) emitting a certain sort of radiation, is not easy. Ayer doesn't really solve the problem; nor, in my view, do more contemporary authors like (say) Frank Jackson. When I was young and overly ambitious I was planning to do so!, but my career has since taken a different and more modest direction.