My primary audience was actually
@Malmuria, who liked the post which I take to mean they understood it. (Given our mutual posting histories, I don't think it means they agreed with everything I said, but rather that they thought that what I said was a reasonable reply to their earlier post.)
"Process simulation" is a phrase that I picked up on these boards, mostly in the context of people explaining why they didn't like 4e D&D (which does not use process simulation at any point). Ron Edwards, about 10 year earlier, coined the phrase purist-for-system simulation to refer to the same thing (4e D&D is about as far as you can get from purist-for-system simulation while still playing a mainstream RPG).
To explain the phenomenon the two terms refer to, we first need to get something out of the way: all RPG resolution systems have the job of
telling us what happens next, in the shared fiction. But they do it in different ways.
The distinctive feature of purist-for-system (= process simulationist) RPGing is that the way the resolution systems tell you what happens next is by modelling the imagined in-fiction causation. They might do this at a fairly fine-grained level (RuneQuest and Rolemaster combat, or 3E D&D grappling, are all good examples) or at a fairly "bird's eye" level (the Pendragon rules for resolving the Winter Phase, or the B/X and AD&D rules for evasion in the wilderness, are examples of this - the former abstracts months, the latter hours, into a small number of dice rolls).
Here's an example of resolution that does
not exemplify a purist-for-system approach; it's a play example of a skill challenge, taken from the 4e Rules Compendium, pp 162-3:
This example shows a DM running a skill challenge for five adventurers: Valenae (an eladrin cleric), Dendric (a human fighter), Uldane (a halfling rogue), Kathra (a dwarf wizard), and Shara (a human fighter). After a battle with a demonic creature that attempted to slay their friend, the priest Pendergraf, the adventurers must determine where the monster came from to prevent another attack.
This 1st-level challenge has a complexity of 1 and requires four successes against DC 12, the moderate DC for 1st level. The goal of the challenge is to find the spot where the adventurers’ enemy, a wizard named Garan, summoned the demon. Garan has hired some thugs to beat up anyone they spot snooping around. If the adventurers fail the challenge, the thugs find them and attack.
DM: You’re left with the last misty remnants of the strange creature’s corpse and a handful of frightened witnesses. “What was that thing?” Pendergraf asks. “And where did it come from?”
Kathra: Can I make an Arcana check to see if I know anything about it?
DM: Sure.
Kathra: I got a 14.
DM (marking down a success for the characters): Okay, you know that the creature was some sort of demon, not native to the world.
<The next check is a failed Perception check to find some tracks. The GM narrates that as the PCs taking some time to find the right set of tracks, and then follows with . . .>
DM: . . . Three thuggish-looking men sit on a bench by the front door. They glare at you as you approach. . . .
Kathra: I’d like to talk to the men to see if any of them saw the demon come by here. How about a Diplomacy check - an 11.
DM (marking the second failure): The thugs make a show of ignoring you as you approach. Then one of them snarls: “Around here, folks know better than to stick their noses where they’re not wanted.” He puts a hand on the hilt of his dagger.
Shara: I put a hand on my greatsword and growl back at them, “I’ll stick my sword where it’s not wanted if you keep up that attitude.” I got a 21 on my Intimidate check.
DM (marking the second success): The thug turns pale in fear as his friends bolt back into the tavern. He points at the building behind you before darting after them.
Dendric: What’s the place look like? Is it a shop, or a private residence?
DM: Someone make a Streetwise check.
Uldane: Using aid another, I try to assist Dendric, since he has the highest Streetwise. I got a 12, so Dendric gets a +2 bonus.
Dendric: Thanks, Uldane. Here’s my check . . . great, a natural 1. That’s a 10, even with Uldane’s assistance.
DM (marking the third and final failure): It looks like an old shop that’s been closed and boarded up. You heard something about this place before, but you can’t quite remember it. As you look the place over, the tavern door opens up behind you. A hulk of a half-orc lumbers out, followed by the thugs you talked to earlier. “I heard you thought you could push my crew around. Well, let’s see you talk tough through a set of broken teeth.” Roll for initiative!
There are at least four ways in which this example of play shows resolution - ie working out what happens next - that is not process-simulationist.
First, the skill challenge framing in itself: the GM is obliged to wrap up the search, be it with a win or a loss, after 4 successes or 3 failures. So resolution is being guided by concerns around pacing and finality of resolution, rather than by concerns of in-fiction causation.
Second, the DCs are being set by reference to a fiction-independent formula ("four 1st level moderate difficulty checks") and not by attending to particular details of the fiction and trying to model their difficulty.
Third, the reason the PCs encounter the thugs has nothing to do with their struggle with the tracks. It's a deliberate framing decision made by the GM to maintain pacing, maintain the pressure and help bring the skill challenge towards its culmination.
Fourth, the GM, in response to the failed Streetwise check, narrates that the Half-Orc comes out with their thug. But that isn't
caused by the fact that the PCs didn't remember anything about the building. The consequences of resolution are not being generated by having regard to in-fiction causal processes, but rather by reference to the demands generated by the skill challenge framework.
Imagine how a scene a bit like this one might be handled differently - eg when the thugs go back into the tavern, the GM makes a morale or a reaction roll for their Half-Orc boss, and uses the results of that roll to decide whether or not the Half-Orc comes out with the thugs: so the Half-Orc might come out even if the PCs do succeed on their Streetwise check, or might not come out even if the PCs fail it. That would be an example of using a process-simulationist approach.