The complexity is dumped into set design, chunky monster actions (like picking people up and throwing them, putting them in strange altered states) and whatever parts of the meta-text might show up in the fight (one monster is special friends with another and gets upset when they die, there are factions within the fight who want slightly seperate things).
A lot of the 'set design' of set-piece Old School fights come down to the stored kinetic energy hidden in elements of the environment.
A PC has to be able to do something to the environment that will unleash stored kinetic energy and hopefully act upon a seperate part of the battle space in a predictable yet unexpected way
Two fictional examples here;
The first is John McTiernan movies, especially the attack on the rebel base in Predator;
If you look at that long scene you'll notice that many of the times when a member of the main cast performs an action to alter the environment, it has an effect which is witnessed, usually by another main character, in a different part of the environment, and which often directly affects it. So the space of the scene is stitched together by this river of movement and action, the characters are connected to each other by kinetic effects which escape their frame of origin.
Die Hard has a bit of this as well, The Hunt for Red October. Not sure about the rest.
And the second is all Pirate Movies;
Thinking about it, its astonishing how much effect the kinetic qualities of a large sailing ship have on the general aspect of Pirate Movies.
(I am looking at the pseudo-kinesis of a heightened fictional pirate movie rather than age-of-sail movies. In real life rope costs money and you want to avoid it being cut, and there are limits to what physics can do.)
A ship as a whole is an environment under complex kinetic pressures, it is an engine designed to harness movement-energy from the sky. It has almost everything we would want from an old-school set-piece battle.
Multi Dimensionality - you can be up in the sails, on the deck, down in the ship itself, or in the sea. All completely different environments, all connected to each other in intuitively obvious ways.
Kinesis - all the ropes are under strain and there is always rope, you can climb up or down, cut ropes and have them pull you up, drop sails or ride them down, swing pretty much anywhere and, most important, almost always tie things to other things.
Meta Elements - a ships crew already has a hierarchy, there are specialist rules, you can see who is in charge, a decapitation strike on the captain or a last-minute negotiation is always a possibility. You are a complex, visible and intuitively graspable social system which the DM doesn't have to spend a lot of time having to explain.
The Pirate Ship even has a built-in 'not-dead-but-largely-out-of-the-fight' status with someone being knocked off the ship.
And the environment as a whole is doing something as you fight on and in it. Several things. The first of which is that it is floating, and if it stops doing that then you are in fucking trouble.
There must be some kind of i
If we were to work backwards, stating that we want kinetically complex and interconnected environments, could we create a kind of ideal concept generator for OSR set-piece fight scenes? What would we get?
Windmills and Watermills - they have the blades or wheel and they have an inside with lots of stuff moving about that could be interrupted and messed about with. They have a big grinding thing you can chuck someone in and ruin the corn. The watermill has a river nearby.
Forges or anything based around fire. Large scale metalworking has those big contained crucibles that can be tipped, possibly channels of molten metal that can be diverted. The annoying ending to the last Hobbit movie had a lot of that.
Actually the 'We're just smelting a giant statue here and its nearly, _right this moment_, finished so don't have a fight here' scene is a good idea. Especially if the giant statue is eeeevil.
Dams or anything holding back a large pressure. Complex lock gates could work as well, though they are rather slow. This is non-optimal as it seems to reduce everything to one disastrous action, but that could be interesting in its own way.
Anything with a living process at its core that has its own logic and could get out of control, or where control of it could be manipulated. Maybe a chemical process like a brewery?
The shipyard with the ship about to launch. You've got the whole business with the rigging, the ship escaping into the water and whatever happens after.
The building site, especially if they are building something tall and *heavy*, things to fall, drop, cut, release, swing on and cause to interact with each other.
Mass transport scenes, especially with = big round barrels that can tip and roll, teams of horses that are straining on things, ropes holding things that can be cut, cranes hoisting things. usually this will happen at a margin between two environments or/and two social patterns, so the nomads of the sand ocean can be shouting at the river-thanes while the giant tortoise gets lose and the glue barrels roll from its back. Giant Animals are a kind of sub-ship only available in high fantasy. Now instead of worrying about the wind or whatever you are thinking about how this big animal is going to react to whatever is going on around it.
A traffic jam in an urban environment might be an interesting space for a big fight.
Of course I've nearly forgotten the parade, which shows up in so many action movies. A huge, moving para-reality acting adjacent to the main one, with its own costumes, roles and its own giant complex objects that it is moving about.
I don't think I've ever seen a D&D scene or fantasy action sequence in a giant protest, with crowds of protesters and law enforcement and all the crap they throw about, even though we have those all the time.
PORTALS! Like every Derping Age (early-21stC) action movie. Someone has opened a portal, and possibly there is more than one, so now we can hop about between the portals and things can fall in and out of them with ridiculous physics affects. Up on one portal side is down or across on another so leaping across _into_ one leads to you falling down out of another
Magic of course lets you replace ropes and tackle with almost any kind of element. Maybe the poetic chanting of the verse monks is keeping this kinetically complex temple/object up in its position and if you interrupt or _change_ the chants then its configuration will shift. Maybe the virgin sacrifice you are here to stop is whats keeping the silver tower spinning in place, but you can only stop it from inside the silver tower.
And I nearly forgot the classic Rope Bridge.
(I throw this one open to the floor.)
Oh, and all this crap is still going on; (FREE BLATHER AT THE BOTTOM IF YOU READ ALL THE WAY DOWN, AGAIN)