In fact, the truly abstract nature of hit points allows the game master the freedom to determine the extent to which realism will be a concern. When a character loses twenty of thirty hit points to a single attack, it is up to the game master to describe the event, and also to decide if there are any effects beyond their loss. To put it simply, the value of the abstraction is in its ambiguity.
I've tried to embrace this vagueness in my Moldvay/Cook/Labyrinth Lord hack game, starting with my own riff on Robert Fisher's Classic D&D Injury Table. But a lot of these little details depend on how you play the game, especially in a text-chat game.
One source for the assumption that every roll of the d20 represents a swing of your character's weapon comes from what we call that roll: a to-hit roll. Right there, I think, is the source of most of our assumptions about "swings" and how hit points are a measure of physical trauma and the like. I can't do much about the decades of labeling TSR and WotC have used, but when I gaming I try to remember to call it an attack roll, and not a to-hit roll. It's a little thing, but I hope it helps to set the right tone and expectations.
I take this same attitude to describing what happens in a fight. Here's an example from Thursday night, when our heroes faced off against a pair of massive, turtle-like humanoids:
The second, smaller creature hisses angrily as it charges at the human. It stabs at him with its spear, again with surprising speed and dismaying strength, and it's all Maythur can do to ward off that sharp flint point with his shortsword. (Maythur loses 2 hit points.)
Again, I don't talk about gashed wounds or near misses. This is ten seconds of combat, a series of dodges and ripostes, feints and slashes. And my models, as much as is possible, are the pulp greats of yesteryear, such as REH:
Her sword darted past a blade that sought to parry, and sheathed six inches of its point in a leather-guarded midriff. The man gasped agonizedly and went to his knees, but his tall mate lunged in, in ferocious silence, raining blow on blow so furiously that Valeria had no opportunity to counter. She stepped back coolly, parrying the strokes and watching for her chance to thrust home. He could not long keep up that flailing whirlwind. His arm would tire, his wind would fail; he would weaken, falter, and then her blade would slide smoothly into his heart. ("Red Nails" - 1936)
The danger with this sort of thing is being too vague. Does the following passage convey that the turtle-man has lost more than three-quarters of his hit points?
Rukmini's attack blindsides the enraged turtle-man, and her first strike bites deep. Within moments, it is now on the defensive, fending off attacks from both of you. The creature, however, seems to go into a berserk rage, slamming its bulk into the dwarf in retaliation and slashing at her with it spear. (Rukmini loses 5 hit points.)
The nice thing about numbers is their lack of ambiguity. Everyone can tell the dwarf is hurting, and just how badly. But I don't think it's very clear that her foe is on his last legs, but one more strike away from death. This is one of those things that constantly challenges the DM in a game like this, and you have to always be honing your technique and varying your style, both to keep things fresh and find new ways to convey what's actually going on, without allowing things to devolve into "You miss, it hits for 5, you hit, roll damage..."