One interesting subtlety is the monster reaction table: upon meeting a sentient denizen of the dungeon, you are meant to roll some dice to see how your encounter goes. And it's perfectly possible that you get along great with some supposedly evil kobold. Nor does this just mean that you don't attack each other. It's an opportunity for cooperation, for plot, for alternate ways of winning that don't involve just killing everything.
Let's take Dungeon Robber, an endless random old-school dungeon crawl. This is no heroic campaign: you are a poor sod with a cudgel who sneaks into an underground labyrinth in the hopes of finding enough treasure to escape abject poverty. Being able to buy a nice house and some land counts as winning. And unlike in e.g Nethack, which is otherwise a far more complex game, each time you meet a sentient monster, you get a reaction roll. And it makes a surprising degree of difference.
And here's another point: in original D&D, it was mostly treasure that gave you XP. Killing monsters gave you near to no XP, and combat was deadly. The loot you sought wasn't usually carried by the creatures in the dungeon, so if you so if you could negotiate or sneak your way past confrontations, you were much better off, and you'd level up just as nicely.
So it would be very interesting to make a "standard" dungeon-crawl game that was nevertheless more about stealth and negotiation. (At this point, of course, I have to mention Undertale, which does allow you to make a completely pacifist run.)
Another thought: physical obstacles. Your classic dungeon is some kind of set of tunnels or corridors, usually in a delapidated state. But the only obstacles you encounter are doors and traps. What about missing stairs, cave-ins, tiny passages meant for tiny goblins, submerged sections, rotten floor-boards, partially rusted-away gratings, etc.
Also, everything is neatly organized into horizontal levels with clearly delineated stairs between them. There's no stony slopes to scramble down, or crawl-spaces below the floors, or narrow ledges halfway up walls, or forest floors with giant criss-crossing roots.
A lot of what makes an "adventure" is really traversing terrain. Think of The Lord of the Rings - yes, the battle scenes were impressive, but the main quest of the hobbits features very little fighting. Most of it is travelling.
Let's go back and think about what a "dungeon" could actually be shaped like - an ancient city half-buried by sand, a giant rotting castle split in two by an earthquake, a set of drainage tunnels intersecting with the caves of an underground civilization, a village hanging from ropes attached to a kilometre-tall mushroom - and who it might contain - seven rat-man cultist factions perpetually at war, the descendants of a doomed dwarven expedition stalked by dust-creatures evoked by their sins, an orc mining operation that uses hundreds of goblin slaves yearning for freedom, a ritualistic society of horseshoe crab people.
Keeping track of complex physical arrangements that can't be separated into neat sections and levels, and of complex societies that can't be divided into "allies" and "enemies" is taxing for a human game-master, which is why even creative settings have a tendency to gravitate back down to being hallways and monsters. But keeping track of things is what we have computers for!
There's a lot of possibilities to uncover for dungeon crawls yet. None of this requires a more complex motivation for the player than "grab loot, escape". The depth can come from the shape and inner life of the dungeon.