Interesting question. I think rigid class structures with zero to hero progression by levels with fixed rewards. Spell lists with hundreds of spells. Magic items as part of the leveling system. Monsters with various fixed abilities and power levels as well as a need to prepare encounters on the Gm side.

DnD5 got rid of a lot of the stuff that 3.5 and 4 did but it still feels like a lot of things that where true about encounter balance are still there.

I think it’s not something as easy as a definition, but an emergent property of many little subsystems interacting, a particular design style and goal, and the gameplay experience. The caveat being, of course, that it also is a completely subjective impression.

There are many things in this new rules system that have already appeared in 4th Ed , yet it would have been a deal-breaker there, like Daily Powers, Action Surges, Second Wind, Healing surges, etc. Here you still have it in well-placed corners of the system, eased up as particular class traits, or dressed up in slightly different prose.

You can also spot several rules that are just there for the sake of carrying on with the legacy. (hellooo Encumbrancy rules!).

For me, what makes D&D “D&Dish” is:

a) The 6 Attributes (those 6 specifically, with a tolerance for a 6th Attribute of “Comeliness”).
b) Levels
c) Strict classes … which carry a ton of baggage (mainly in the minds of the fans, and not necessarily in the mechanics itself … for example, there’s nothing even remotely wrong with ditching the Paladin and just having a Fighter/Cleric, moving some of the Paladin’s abilities around …but suggest that in certain fan circles, and they’re incapable of treating the Cleric in generic enough terms to have it overlap with the Paladin … even though, contrary to 1e mechanics, the Paladin is absolutely a subclass of the Cleric).
d) weak skill system (3e probably had the strongest skill system (before 5e, not sure about 5e), but it still didn’t put attack abilities under skills; D&D skills tend to feel like this second class citizen thing).
e) a strong differentiation between how monsters are built vs how characters are built (3e tried to bridge that, but it always felt awkward).
f) spell slots (probably the reason 4e felt very unD&D to me).
g) hit points, and the hit-point/healing-magic economy, and their odd implications about abstractions wrt to damage vs luck vs fatigue (ie. a hit is not always a “hit”).
h) Armor Class, how it’s handled, and its implications.

All of those things together typically spell a D&D-ish game, to me. And you typically find those sorts of things in D&D knock-off games (not just retroclones, but actual knock-offs). But, those things all vary when you cross over to, say, Rolemaster (weak classes, strong skill system, armor and “hit points” are completely different, no spell slots anywhere, and a very different Attribute system … but still very level based and still with a strong differentiation between monsters and characters). And, mechanically, Rolemaster doesn’t feel very D&D-ish (to me) at all… even though it started out as a set of extensions for D&D.

(I meant this to be a quick addendum to my list of D&D-ish things, but it turned into a much longer essay — sorry)

Oh another thing that makes D&D “D&Dish” to me, which sort of continues on the “weak skill system” is that fighting ability and spell ability are completely independent of the skill system. This is a legacy of how attack ability and spell casting ability were tied to class, and somewhat to the way the first skills (thieving skills) were a completely separate mechanic … and then later expanded by yet a 3rd mechanic (non-weapon proficiencies).

Again, using RM/SM has a counter example (because it is also class and level based), non-weapon skills and weapon skill are both part of the same skill system (it’s just easier/cheaper for fighting classes to develop them). Spells also have some skills that are part of that same skill system, and knowing a spell at all eats some of your skill points as well. So, spells are also, both directly and indirectly, part of the skill system (or skill point economy). Even hit points are part of that same skill point economy.

Other games are typically even more uniform/regular about combat ability vs spell ability vs other skill abilities. D&D has historically just been rather odd and irregular about how it implements these three things. And that’s part of what gives D&D it’s feel, to me — the lack of ability to directly interchange fighting ability, magical ability, skills, and potentially hit-points.

This next bit is more cultural than systemic, but it is also partially systemic. AD&D (1e) started things down the path of codifying everything, and fixing how things are done within particular rules. This also made things less flexible, and less left open to interpretation … and that has implications about the stories you can tell with AD&D, and also the stories you can (or can’t easily) adapt to AD&D’s lineage.

In D&D (in general, not just AD&D’s lineage) Fighters and Thieves are two different things, not just a “non-spell caster who leans more toward fighting or more toward subterfuge” (for example, before the official AD&D Barbarian class was released … there were endless debates about whether Conan was a Fighter or a Thief, and he couldn’t be both because he was human, and not really “dual-classed” … and the only way to really fix it was to put a bandaid on it by creating a new class (an admission that the existing classes weren’t sufficient)). That has an effect upon the stories you can tell, because the story has to fit that false dichotomy. Similarly for wizards vs clerics. Or, more strongly, for clerics vs druids. Or having to fit your fiction around the idea of spell slots (and dealing with inconsistencies about modeling fiction that doesn’t work with spell slots). These false differences then creep into everything.

Every game has that to some degree, because the system defines the “physics” of the game and thus the game-world. But D&D’s quirks have, in my experience, more directly “gotten in the way” of those things. The result is that D&D based game worlds all have similar feels to them, partially imposed by the quirky mechanics. Whereas, game worlds based around less-quirky game mechanics seem to be easier to adapt to other less-quirky games (and not as easy to adapt to D&D)… that sort of feeds into what makes things “D&D-ish”.

To give you an example of D&D rules that don’t fit this pervasive presence of false dichotomies: around the time 3.5e came out, Unearthed Arcana published 3 “generic classes”. I never met anyone (other than myself) that viewed them as actually playable classes, as opposed to a way to build a new class. Yet, these classes were in fact completely playable, as long as you shed the typical quirky mindsets of D&D. You don’t need two or three different spell casting classes, “Spellcaster” is enough. You don’t need N different fighting classes, 1 class that focuses on combat is enough. And the paladin is just someone that multiclasses between Spellcaster and Fighter (more toward Fighter). But, no one really embraced that because it didn’t feel D&Dish to use those rules in a “rules as written” way. Which supports what I’m saying about the quirky and somewhat arbitrary dichotomies in how D&D does certain things: if you get rid of those dichotomies, even within the D&D system itself, you lose the D&D feel. And that doesn’t get embraced by the D&D core fan base. (and, I think that’s somewhat what happened with 4e, as well)

I’m not knocking D&D, mind-you. The 3e family is still one of my favorite RPG’s ever. Even with its clear limitations. I’m currently on a bent to mix FATE and OSR, because I think the BECMI D&D had some superior wisdom compared to AD&D, and is a fine boilerplate for RPG’ing in general. I wouldn’t be bothering with that if I didn’t feel that D&D was positively influential upon the history if RPG mechanics. But, that doesn’t mean I ignore its quirks, or what makes D&D feel “D&Dish”.