I think your initial post and list really hits at the "core" of what D&D is/why D&D is D&D and other rpgs are not.
The 6 abilities (SIWDCCh, and yes, that is the "correct" order

)
The core/"big" 4 classes: Ftr, MU, Cle, Thf.
HP -not "health," not "life points," not anything else. "Hit Points."
Saves are core and indispensable to the game....whether that is most efficiently 3 or 6 or differentiated by class or race or what have you. Saves have to be in there.
I think the arcana of the time[-ing] system is worthy of a mention. Rounds v. Melee Rounds. How long? How many rounds in a turn?You mean a "turn - 10 minutes" or "it's my turn?" How many rounds in a minute? How many turns in an hour? How many what where now? They shift. They change. They make more sense/have been cleaned up or streamlined more than they, perhaps, were. But I feel that getting your head around the measuring and imagining of time that passes in "in game" time is decidedly a "Why's D&D D&D?" thing.
I would add the "core" species. Humans, elves, dwarves, halflings. Ripped from Tolkien and all, they've been there from the word go. Without those 4 (at least), by definition, it "can't" be D&D.
I would also add, for all of the flack it gets and it seems everyone likes to ignore it these days, Alignment "makes D&D D&D." At least on the Lawful-Neutral-Chaos axis is a quintessential and purposefully included in D&D thing. Other games/systems do it too...Why? Because it's always been in D&D. The [whether purposeful or accidental or reluctant] "heroes" going up against the villains, the "Forces of Good" saving the day/world/multiverse from the "Forces of Evil," is essential to not just fantasy role-playing games, but a good story of/in any milieu.
EDIT TO ADD:
The separation of magics/spells between MUs and Cles....and thus carrying over/through the game in all incarnations, whatever the titles/names for them. Other systems use different magical organizations...either teased out into every possible different facet/contingency or different magics based on magical practices, to the all lumped together (a la some neo-pagan/modern day idea) of "all magic is magic" with spells divided by ethical or moral intent, i.e. "white/grey/black" magic, or other thematic groupings ("blue" magic for the air, "red" magic for dealing damage/blood/war, "green" magic for nature/plants, etc...) and different character classes/concepts use whatever "color" of magic best suits their individual flavor. But all of that has blossomed and branched and interwoven over the decades all began from the simple idea that a "wizardy guy" has/used different magic [different spell list] from a "priestly guy" and nary the twain shall meet...though nowadays they meet, maybe, a little here and there.
/EDIT