Dividing DM from the mechanics when there is a rule that says they're part of them is taking a view on what counts as mechanics. It's drawing a limit around how far DM can go in fulfilment of the rule and excludes that DM completing a rule may be properly counted part of system.
I think you are reading too much weight here into relatively informal ways of speaking. Or imposing your own formal meanings onto those (like me) who aren't following them.
As I'm sure you know, Edwards follows Tweet in dividing resolution systems into karma (compare numbers - eg the example given upthread of comparing two passive scores to find out if someone is surprised), fortune (rolling the dice) and drama (someone gets to say something). There can also be processes that "toggle" between resolution systems - Edwards gives as an example Prince Valiant, which defaults to fortune resolution but sometimes allows a participant to trigger a "special effect" (players do so by spending storyteller certificates; GM's do so by referring to the details of their prep) which then substitutes drama for fortunes.
By
mechanics I mean a "mechanical" process that is part of the resolution system: rolling a die, looking up a chart, spending a chit/token/certificate, etc. "Mechanical" here means "in the nature of a machine; deterministic". I do not describe a person using their discretion to introduce some new fiction by way of narration as a mechanical process. It may be enlivened by a mechanical process (eg the spending of a storyteller certificate). It may enliven a mechanical process (eg I say that "I pursue the bandit" and the GM then calls for a roll). But it is not itself a mechanical process.
In separating GM narration from
mechanical processes - and contrary to what you attribute to me - I am not drawing a limit around how far the GM can go in the fulfilment of a rule, nor saying anything about what may be part of a system.
To bring this back to "simulationism", here's an example of play (from Prince Valiant):
There was talk of a powerful knight who was blocking the road north, not letting anyone pass who was unable to beat him in battle - and so far unbeaten. (This was Sir Lionheart, of the second Challenge from a Knight scenario in the rulebook.) Naturally the PCs headed off to see if they could do better, with a crowd in tow to see the excitement and the performer working the crowd.
<snip>
The PC asked for a joust, but the proud Sir Lionheart declined to joust with a mere squire. To which the PC responded, "Fine, I'll just continue on my way then!" and tried to pass Sir Lionheart and continue along the road. This called for a Presence vs Presence check, which the PC won - and so Sir Lionheart knighted him so that he could joust and perhaps succeed where the others had failed. I took the words of the knight ceremony from Excalibur - "In the name of God, St Michael and St George I give you the right to bear arms and the power to mete justice".
The player of the (now) Sir Morgath determined that he would use his certificate for an outright victory. He considered knocking Sir Lionheart senseless, but he suspected (correctly, as it turned out, given the scenario description) that if he unhorsed Sir Lionheart but didn't kill him, Sir Lionheart would insist on fighting with swords to the death. So he decided to Kill a Foe in Combat - when the lances of the two knights connected, the one wielded by Sir Morgath splintered, and a shard flew through a gap in Sir Lionheart's visor and entered his brain through his eye, killing him!
Sir Morgath was feted by the crowd.
In this episode at first there is free roleplaying - conversation back and forth between player and GM, some in character and some describing actions. This leads to a conflict: Sir Lionheart has refused to joust with the squire, but also does not want to let him pass. And so fortune resolution is used, and the player wins, and so the squire has persuaded Sir Lionheart to knight him, so that he can joust to try and earn his passage past. This then leads to more narration: the two knights mount and charge one another. And then the player decides to spend his storyteller certificate to Kill a Foe in Combat. And he narrates -
drama resolution - how this happens.
The player narrating how Sir Morgath defeats Sir Lionheart, despite Sir Lionheart being the far better knight, is a "completion" of a rule (as best I understand your use of that word in relation to the GM). But it is not remotely simulationist, if
that word is to have any distinct meaning. Given that all RPGing involves the creation of fictions by way of a process, the fact that a fiction has been created by way of a process does not make the game simulationist.
One aspect of enjoyment of D&D indeed lies in witnessing the mathematical structure of the game engine in action. Optimizers are sometimes mistakenly understood to be trying to win harder, but some optimizers are simply engaged by the dynamic mathematical structure of the game. The combat minigame provides an ideal arena for witnessing the game engine in action... seeing how choices in the chargen component play out. What counts as an "enjoyable mathematical structure" is subjective: what one ends up saying is that certain games had mathematical structures that one found enjoyable for their own sake.
To me Tuovinen introduces some uncertainty in what he means when he writes "Games with heavier rules have a potential to support the players in maintaining and performing a more detailed and definitive Exploration state." So now it's not about enjoying witnessing the game engine in action, it's about maintaining and performing a detailed and definitive exploration state.
I don't think that Tuovinen introduces uncertainty. I think it's pretty clear which RPGs he has in mind.
In talking about the maths of D&D, you seem to me to be ignoring something that Tuovinen takes for granted: namely, that RPGing involves the creation of a shared imaginary space. In "mechanical simulation", the mathematics that is attended to is contributing to, and modelling, a SIS. Rolemaster and RQ are examples: the numbers aren't just manipulated in the abstract, but rather the manipulation of the numbers and the sharing of a fiction go hand-in-hand. This is not the case for the D&D minigame: which is
@Hussar's whole point!