What about damage to a wraith or spectre?
Well, at least you've given up on attempting to prove that damage to a person from a weapon doesn't involve tissue damage since the TEXT PRETTY EXPLICITLY SAYS IT DOES.
It's not clear from the text what wraiths and specters are made out of, but since at least magical weapons can cut it, it's got at least some physical substance. Ectoplasm maybe. Whatever ethereal things are made of - ether presumably. Or at worst, an energy field, which while intangible is nonetheless physical. Regardless, whatever the substance, from the general explanation of hit points, it's clear that if the sword whiffs and doesn't touch the substance of the wraith, it doesn't do damage and if it did do damage we know that it is because it can cut whatever wraiths are made of.
What about damage caused by psionic attacks against psionics with no points left to deplete? (Is the tissue in their brains being damaged?! And then heaing via a few days rest?!)
I'm not hugely familiar with the psionic rules in 3rd edition, and I'm not familiar at all with the 2nd edition rules. However, if you look at the 1e table one thing that stands out quite glaringly - psionic attacks by and large don't do hit point damage. You can be dazed, confused, rendered an idiot, turned insane, paniced, enraged, stunned, killed (your mind physically crushed), temporarily or permanently lose psionic power, put into a coma, or rendered a will-less robot but normal psionic attacks don't do hit point damage.
So far as I know (and I admit my knowledge of 3rd psionic is quite limited, since I never embraced them, seeing as they were offered only as an alternative magic system) psionic combat was removed from the game by 3.5, but in general psionic attacks in 3rd edition for the most part did ability damage or put debuff conditions on the target very much like 1e. Those that do hit point damage, say psychic crush, presumably do physical damage to the brain - they explicitly did so in 1e. In fact, because by the definition and explanation provided for hit points, which I've already provided, we pretty much know that if some hit point damage has occurred, at least some physical wounds have also been sustained. The target may or may not have also lost some amount of metaphysical resources as part of evading the brunt of the attack, but if damage occurred the attack was by definition not completely evaded and some damage occurred. This is not only logical from the words 'hit' and 'damage' - to say nothing of the logic of the phrase 'hit point' itself - but explicitly stated by the text.
Again:
"Each hit scored upon the character does only a small amount of actual physical harm - the sword thrust that would have run a 1st level fighter through the heart merely grazes the character due to the fighter's exceptional skill, luck, and sixth sense ability which cause movement to avoid the attack at just the right moment. However, having sustained 40 or 50 hit points of damage, our lordly fighter will be covered with a number of nicks, scratches, cuts, and bruises. It will require a long period of rest and recuperation to regain the physical and metaphysical peak of 95 hit points." - Gary Gygax
If 'hit points' were meant to express something that could be lost without hitting the target, why in the heck did they decide to call them 'hit points'? I mean sheesh, the mental back flips that some people are going through in this thread to not see things by there most obvious interpretation astounds me.
I'm not even sure that damage to a skeleton or zombie is aptly characterised as tissue damage, any more than damage dealt to a door by an axe or to paper by fire is tissue damage.
They may be things, but they definitely have tissue. Bone is a tissue. 'Tissue' in a medical sense just means the structural material something is made of. And in the sense I'm using it, by tissue I mean 'the thing that the creature is actually made of' as opposed to 'any and all other metaphysical things that hit points abstract to not limited to skill, luck, destiny'. So in the sense I mean it, the 'tissue' or 'meat' of an iron golem is 'animated iron'. This would I think be pretty darn obvious, and in any event even if my words 'tissue' and 'meat' are unclear and insufficiently generic, none of that would disrupt understanding of the very clear meaning of hit points.
I mean basically we are given a very clear and exacting explanation of what hit points are meant to represent in the text by the author of the system, and this interpretation has been in throughout all the other systems that have readily adopted the concept of the hit point from pnp RPGs to side scrolling fighter video games, and so what you probably should be doing is trying to understand how the ill defined wraith must fit into this clearly defined system, rather than using the using the gaps in the explanation of 'Wraith' to argue that the system is other than how it is has been explicitly defined.