Since I've been mentioned several times (and it's not late at night and I've had some caffeine

) I thought I would clarify my thoughts. Short version? Simulation models a flow of possible events. In D&D it's modeling the reaction of PCs to events in a fantastical world.
I think any system that broadly gives the impression of mimicking the environment, world, events we're trying to to evoke can be considered a simulation. A technical definition of simulation can be found
here "
A simulation is a model that mimics the operation of an existing or proposed system, providing evidence for decision-making by being able to test different scenarios or process changes." Another relevant sentence "
Any system or process that has a flow of events can be simulated." Many of the things raised as reasons why D&D is not a simulation is never mentioned in any of the general definitions I can find. There's no mention of the various subsystems telling us
why those subsystems acted in the way they did, it's all about what we are simulating reacting to those subsystems.
Your own first proposed definition answers this. A simulation needs to 'mimic the operation of an existing or proposed system'. I think that all of my objections are based on this particular phrase, or the general 'is a model', or perhaps some flavor of 'being able to test different scenarios'. That third one I find many putative simulations fail on based on the fact that they are so simple they don't really admit of different inputs. I'd also note that something like an encumbrance model doesn't seem to have much of a character of 'a process that has a flow of events' to it, being simply a static model, though I'm less concerned with that as it could at least serve as a component input to other processes which might be simulations of something.
Now, obviously the article I found after 30 seconds of googling is about simulating the real world but the key to me is that you're just mimicking something, a flow of events. So I consider the
Fallout games a simulation of a fictional post-apocalyptic world based on an alternative 50's vision of the future. That doesn't mean I believe radiation can make magical mutants or that the power armor they use is realistic, it doesn't need to be. If you use the VATS system, it becomes obvious that every time you shoot at someone the game is rolling percentile dice in the background to see if you hit. It doesn't "justify" why you hit, it just rolls the digital dice. Much like when an attempt to climb is made we role the polyhedral random number generator.
Sure, but does their combat system really, in a meaningful way that corresponds in some degree to reality tell you what factors are really relevant in terms of the overall lethality of gunfire in different situations? In other words, could you look at the model, or run the simulation with various inputs, and extract from it some useful and predictive output that would inform decisions in the simulated type of situation (IE when setting up a real gun battle for instance). My guess, having played one or two of these games, is that it would be of very marginal use there, but that it is at least moderately good at generating (along with other inputs from participants) a suitable NARRATIVE of a gun battle. It seems far less like a gun battle simulator and far more like a narrative generator. I mean, you can certainly go ahead and talk about it in simulation terms, but I'm skeptical that is the most effective approach. For instance, things that are likely to make it a better simulation are unlikely to make it a better game, nor perhaps to improve the narrative in terms of the qualities that are likely valued by the participants.
However, I think the questions I'm raising fall well within the realm of what and why the OP's original question was aimed at discussing.
The flow of events is what we are simulating. It's how our PCs interact with and respond to a fictional magical world. When I play D&D I'm not running a rock climbing simulation. I'm simulating the attempts of the PC to overcome obstacles which may include climbing a wall they cannot automatically climb. The results of that attempt to climb and what happens to the PC on success or failure is what matters. If Bob can't tell that Sue is lying but Alex could have, it's just simulating the fact that in this specific instance Bob wasn't paying enough attention or is not very good at reading people. Whether the people at the table add fluff to justify why Bob wasn't paying enough attention is just decorative narration, it doesn't change the outcome. The game's simulationist aspect is not altered by the fact that we also add narration.
Right, this is why I call these games something closer to narrative generators than simulations. They are not really concerned with accuracy. The primary concerns involve how, when, and where the participants make inputs, the comprehensibility of the situations portrayed and how they can be reasoned about, and then about other non-narrative aspects like how enjoyable the game process of play itself is.
As far as dragons, the fiction for dragons in D&D is limited to the rules of the game. Dragon lore varies so widely there has to be some baseline. Some dragons are small crocodile sized that St George slew, others are basically gods that can consume stars. I use D&D's baseline as established in the MM. That means that at a maximum they have an AC only slightly better than a PC in plate with a shield. That AC can be matched (or exceeded) by magical enhancements a PC would normally have at high levels. Even an ancient red dragon only has a little over double the HP of a 20th level barbarian (assuming 18 con). Hard to kill? Absolutely. It's why a lone PC would probably be literal toast. Impossible to kill? No, not according to the fiction established by the rules of the game*.
5e dragons seemed pretty darned tough and BIG to me when I have seen them depicted in play. Outside of some significant trickery mid-range 5e dragons didn't seem to be something you could really defeat at all in a practical way. One thing our encounters drove home in spades, you better approach it on your own terms, because if the dragon gets to pick how and where it fights you, then its pretty much game over.
Are high level PCs in D&D supremely good at what they do? Even exceeding normal (real world) human capabilities? Sure. That's part of what we're simulating, a world where the best of the best can indeed face down dragons. At times it's a very crude simulation, one that has many simplifications and limitations because it's a TTRPG.
Right, but a 20th level Battlemaster actually is NOT significantly better at Athletics than 'ordinary humans' by the rules as written. That was the issue discussed, if you can actually defeat a 10 ton dragon, you couldn't possibly lose a contest of strength with any sort of realistic ordinary human.
In any case, that's my definition, backed up by definitions of what simulation means outside of the gaming world.
P.S. If you want to have a discussion that's fine. If you want to tell me I'm wrong because of some definition of simulation you've established I probably won't respond. If you can find some non-game-theory definition of simulation reference that contradicts what I've said, I'll take a look when I have time. I'm not being dismissive of other people's opinions, I just don't see the point of saying "you're wrong" vs "no, you are".
*Although in my games I rarely use high level dragons because unless there are unusual circumstances I would use tactics that would likely kill off one or more PCs. They're more than just a static pile of HP, but that's a different discussion.
Well, if people have a discussion where they don't agree on certain points, then the only reasonable and fair tactic is to point out where the other person's logic falls short in some way, right? That and/or making some alternative argument are the only two approaches that seem possible to me.
I mean, I don't have a problem with the definitions you put forward at the start of the post, but I believe they are entirely consistent with, and congruent with the ones that I put forward myself! So, my main observation is that it doesn't appear that RPGs, most of them at any rate, are terribly concerned with simulating anything. They seem concerned with providing a recognizable depiction of the ordinary world outside of whatever conceits they are adding. You can, to some varying degree, apply the definition simulation to some of those. The problem as I see it is that simulation in general has a focus on making a useful and faithful mapping of real/potentially real scenarios back and forth onto its models in order to create predictive power. The agenda there is heavily in the direction of improving the quality of that mapping with the understanding that it will both increase predictive power, and potentially generate insights into the physical system being modeled.
IMHO RPG depictions don't really have the above simulation agenda. Honestly, games like Aftermath showed us this back in the mid-80s. You can make really detailed models of things (guns in this case) and then deploy them in the form of a really complicated combat system, but the result is not a materially better game experience than that had by playing something like Traveller, at least for most people. I mean, there were a bunch of serious gun heads that loved Aftermath, but I found the play in that game really rather dull myself. So, my general advice to game designers and GMs, certainly in terms of 'simulation of process' kinds of things (like use of skills or combat) is to focus more on how the depiction works in game and narrative terms, and less on worrying about how it maps onto the fiction in a mechanical sense.
Finally, I don't even think that simulation is actually the concern for most people who are using the term. It seems more like the most common concern has more to do with how the process incorporates or does not incorporate elements that are present in the fiction, amongst other concerns. So, for instance, even though something like an inventory subsystem that produces results more likely to objectively mimic the outcomes of experienced characters choices of equipment might seem to be a better simulated inventory by any reasonable definition of simulation, it is selected against for other reasons like its effect on how and when the narrative unfolds. It feels super hard to have any scope for discussion of how depictions work in RPGs with that in mind since any but one very narrow set of mechanics is met with scorn from some direction or other.