Celebrim
Legend
Second, D&D today is not defined by its ruleset alone.
Great post, and there are a ton of things I could discuss or elaborate on, but I want to pick out that one to talk about why D&D is weird compared to the modern RPG experience. (But in the end how that only matters a bit.)
First, no tabletop RPG is defined by its ruleset alone. How you prepare to play the game and how you think about playing it is just as important than the rules. The rules inform the processes of play at the table but they don't define them.
Two big things contribute to D&D's weirdness.
First, the creators of D&D did not set out to create a particular type of game or particular kind of experience. They were as Jon Peterson said, "Playing at the world." They were to try to simulate whole worlds in their totality with no preconceptions about what their games would be about. Indeed, the focus on dungeons was something of an accident, and not even Arneson's original intent. Dungeons were intended as a minigame that ended up becoming the main game through player interest and demand. The result of this lack of preconception was that D&D rules were more organic than planned, arising from the need to solve problems as they came up in play with no prior guidance as to how problems could be solved. The D&D rules were "rulings not rules" in a way that no subsequent game could be, because the D&D rules were the ultimate example of ruling codification. Every single rule had at one time been a ruling that became standardized through play. And indeed, that might be overstating it, because in 1981 the game's co-creators were still experimentally altering the rules at their own tables. AD&D's 1e DMG is a disorganized record of possible house rules that Gygax is using or thinking about using at the time, some of which would survive playtesting and some of which he likely soon discarded as not really workable.
And secondly, the process of play of D&D wasn't strongly codified. It's really only in the last 10 or 15 years that the designers of games have started to realize how much traditional RPGs left unsaid about how to play the game and designers started to codify the basics of processes of play into the rules. How to play an RPG much less this RPG wasn't really codified in the rules. What D&D however did probably better than any game then or since was provide examples of play. That is, in the 1e DMG there are several pages devoted to a realistic description of one possible process of play using the rules in the book. But even more so, the actual meat of the D&D game wasn't in the rules but in the modules. The modules codified not only the preparation for play, but also some of the processes of play and in many cases also rules. It was the adventures as interpreted by the DMs that taught people how to play - including the DMs. And since the modules all differed in their rulings and processes of play, how you learned to play and how you handled different situations all differed.
The three different rule sets only added to the variation, as a GM could learn with one rule set, then move to another adopting portions of the ruleset and not others based on an adaptative process without realizing that a particular rule or process of play changed subtly between the three in print editions.
No modern game is going to function like this. The rules in any modern game are going to be written to a standard of completion before the game is ever played. And the designer is going to have a vision of what they want the rules to be (or to not be) that will be informed by existing rules sets. No serious modern designer is going to neglect the importance of process of play and if they are trying to achieve a particular game will go into great detail about such things as to how a social challenge is to be handled in the general case, or how to handle the case of searching for clues or loot with respect to player skill vs. character skill.
That said, I maintain that this is merely a difference of degree and not of kind. First, because no RPG can be defined by its rules alone, and secondly because no GM is actually constrained by the rules - least of all an experienced one, least of all one that grew up on traditional RPGs. (But even an inexperience one will be unconstrained by accident, simply because they will make mistakes and invent their own processes of play in ignorance of the rules and the designer's intent.) I can learn to play a modern RPG by sitting as a player at the table of that RPG's author, and yet no matter how well he communicates his intent regarding the rules and processes of play, if you sit at my table you will end up with a slightly different game both by intention and accident. I will decide that there are particular frictions in the rules I can't tolerate and so will want to change with house rules, and at the same time I will have different judgements and incomplete knowledge of the rules that will lead me off into my own version of the game.
So while what you say is true of D&D and is true to a very great degree, I think the argument you advance is also true to a lesser degree of every single RPG. D&D is weird, but it's also weird in the way every RPG is also weird just necessarily more so.