I thought the rest of the post you are responding to adequately addressed this. Representations such as hit points can then feed other rules and/or dictate that certain things should be asserted in the fiction. Since my example was only hit points, a D&D mechanism, I didn't try to describe all the other possible variations of 'harm systems' as it wasn't germane to my point. In any case, I agree that there are many such variations and they often have a more direct and concrete linkage to fiction.If one is playing by the letter of the RAW, agreed. In practice, however...
They can and do affect the fiction state, in some games directly, in others less so.
Note that not all HP based games are as "Go... Go... Dead!" as the pre-3E D&D, nor even as much as 3.x/4.x/5.x with "Go... Go... Bleeding but Go... Dying... Dead"
Twilight 2000 4e (Year Zero Dice Step), PC's have single digit HP, and weapons typically do 2+excess successes (ExS) with 1+ExS to 3+ExS being typical for man portable firearms and melee weapons. The amount post armor (usually 1 point over base, sometimes 2 or 3 over) determines if a critical is applied. If HP are zeroed, a critical is applied. If both happen as a single attack, roll twice and take the worse crit. Further, at 0, one goes down.
One of the PCs, SSgt Morton, on the mend from a 5 HP hit that also caused a brain hemorrhage. The mechanics for crits directly placed two elements into the fiction: he's not mentally as clear as he normally is, and he needed food, water, and rest. (Prerequisites to get the HP back.)
He was jumped on watch by a couple traitorous NPCs. He had gotten all 5 HP back, but still suffers the major Int & Emp penalties. When he'd been jumped, he had taken 2 of his 5 HP again... and it majorly shaped his choices, as the player knew Morton's one good hit from dying. The HP and armor mechanics and combat procedures took my narration, "SGT Toebel charges you with a fixed bayonet" and added the following narrative elements: That he hit, but hit the arm. That it was a minor wound (no crit), and that SSgt Morton was still conscious and did not have to flee.
Took less time to resolve it than it took for me to type it up (~10 min typing, about 3.5 min to resolve).