The best thing for me about Old D&D and its clones (and what brings them over any other games) is, in my opinion, how they are the only rpgs that care about procedural game generation. That is: you have a looping mechanic that keeps the game forward, by the chemical reaction of the PC's advancement rules (XP for gold) and the dungeon stocking chart (or hexcrawl generation chart). As long as you have this, there is a game going on.
This allows the GM to wholeheartedly assume the role of a "referee", instead of burdening him with the tasks of being an Omniscient God, a plot writer, a world builder, a wise mathematical balancer and fun enforcer. I'd say even more: He is allowed to be all these things whenever he wants (you can build a dungeon manually, or even build a complex, dungeon-less adventure) but you are not forced to. If the players go on an unexpected way, or if you don't feel creative at any moment, you can just fall back on the pure game: let them do it! it is built for that. In a sense, (old) D&D is the only rpg that provides you the game rules AND the game.
This is something that all the 90s books that came after failed to understand. Games like L5R or Vampire give you only the game rules. Then they give you a 300 page lore brick, from which the GM must make the game himself, having to rely on "mission" based sessions to play. Well, this is not something impossible to do: I'm sure there were and will be many successful campaigns with that! but it lacks the mechanical structure to support the game on itself and the point of playing it becomes abstracted or null once the GM pulls the foot 1 gram from the gas pedal. In a sense they are exponentially much more "GM demanding", specially if you are not heavily invested into their worlds. (This, of course, is something that capitalism fixed quickly by selling you modules and splatbooks).
This doesn't even make them better suited for story-based games. Actually I think D&D is still better at it: you dont have the pressure to control everything, which in turn opens the possibility of a sandbox and freedom of choice for the players. This makes any plots you actually want to use a nice story to be explored and played with, instead of a fragile railroad that must be protected against the player's actions. And, underneath all of it, you feel that you are in a fair fight against the odds, with no helding hands by the GM. This is, for me, what makes the OSR distinct and OD&D the king of rpgs.
I'm not saying that it is the only way, though. I am sure that mission-based games could be systematized too. The core could look like a mission generator that would... (just brainstorming);
a) generate quests appropiate for the PCs and tone of the game; maybe even let them choose between various missions; each one with some definite "end state", whether succesful or not.
b) generate as many details of the whole quest as possible, prioritizing the spots that the game wants to show or test. Some games might allow or even encourage player's input on what is going to appear
c) a mechanic that determines how does your character and/or the world change after the quest is done or failed. This can take the shape of leveling up, something more or something else (game-world progress based on character actions is something that is rarely coded in rules, and I make this note for myself in order to explore this in the future)
DnD 5e and many allegedly OSR hacks such as Knave, Maze Rats, etc also fall in the second type of games. The case of Dungeons and Dragons Fifth Edition is specially painful as the game is 300+ pages long and manages to cover neither mechanics for the game loop nor a setting, beyond the implied on the monster manual. Its just rules and rules and rules but no real structure behind it. (I frankly cannot understand how people manages to play it without handwaving 90% of it).
I have loved, still love and even made some ultra light rpgs (I use to collect all PDFs I can find); but after this revelation I realized that most of them make no attempt to provide gameplay beyond Character Creation + Combat + Skill checks. Which again, can be good and can work with a GM wanting to do all the rest, but now I feel as a designer that focusing the same amount of rules in mechanically enabling a specific biorhythm is much more interesting. You can change or adapt the resolution system of any game and make it work much the same (for example, the 2d6 hacks of D&D or using point buy vs random generation) and while the chances of success/defeat could vary, the nature of the campaign would not.
This is why I think the term CORE RULES suits better my idea (the rules that enable the intended biorhythm and create game) than the idea of conflict resolution rules: A core is something deep that cannot be changed without changing the whole thing in the process.
To close this post, I will run over some games (no particular order or reason) and see which of their mechanics are centered on bringing the game forward, which in my opinion is their most important rule:
Everyone Is John uses the other players actions as the current player's obstacles, so the game is actually generated by your friends. The core rules are those that focus on switching the control of John. Conga Mummies is a boardgame version of this approach.
Ghost Lines has got a very nice mission based generator that activates once the PCs get side jobs. The actual ghosts are generated collectivelly by asking questions to the players. It also features an astonishing collection of missions, ghosts, employeers, city events, implied setting, etc for a game so small, Definitely an inspiration to have as reference. Check out this fan-made variation using chtulhu dark's resolution system to further prove my point that the core rules of a game are not related to action checks, but for content generation. Some other games like Lasers and Feelings also uses a random mission maker but doesnt really create a solid framework beyond an oracular prompt.
Lady Blackbird, by the same author as above, uses a really cool way of unlocking character abilities: You all play named, premade characters; and advance in power by advancing your personal plot towards certain points, so it makes gamist fucks like me to advance the plot whether you like it or not, making also things change for the world and everybody.
Ryuutama has a clunky and weirdly complex unique way of handling most things (stamina, travel, magic), with the GM ability to influence the outcomes of the party in the shape of a ryuujin (dragon spirit guide more or less) being a really, really cool and original thing. But none of them answer once the pcs ask: "What now?". The game has prepared for that with another sub-section: The collective city and world builder guide, and the adventure writing guide (basically guidelines on how to write an "episode" of which the PCs will be part).
Apocalypse World and its derivatives use the list of fronts, which trigger sometimes on failed moves, and a set of principles which act as a subjective proxy for "genre fairness" (evidently we are all human and might interpret principles differently). While this can certainly work, it becomes much more streamlined and concise on small PBTA games such as Sagas of the Icelanders than in more generic like Dungeon World, as the moves they invoke on a failure tend to be more specific and carry more narrative weight. Check World of Apocalypse for an actual flowchart of the game pace.
Into the Odd (full edition) has a similar approach to B/X, but with advancement being earned each mission (the game defines a mission as "going out and returning with something worth showing"). Curiously, the One page edition of ITO has a very cool dungeon and random encounter generators that can completely map your first quest; and might serve as a base to build new generators for the next ones.
And, making a callback to a recent entry, Pokethulu might pull you in for the very sake of catching new pokethulhus, (much like the original game, that is what I call faithful adapting), so as long as a monster exists and the PCs want to catch it, you only have to put it somewhere on the map, then put more trouble on the way. Still, in my opinion its a game that would really benefit of having random encounter tables, proper hexcrawl rules adapted to pokemon travelling speeds and capabilities (like flight, swim, run, dimension bending or others, really, this could be awesome) and little more power granularity between monsters. But maybe I will take care of it someday. I guess that their creators never thought that somebody would ever take so seriuously what they believed to be a joke game!
Basically we can conclude that there are (at least) four ways from which game content can be brought to the table:
1.Procedural generation
2. Taken straight from a book (such as monster manuals, using a pre-written adventure or following Pendragon's campaign straight)
3. Created communally by the table or
4. Leave it to be created by the GM, this last one being the most used by commercial and indie rpgs alike, with more or less "guidance" from the book.
This methods of course can be mixed in different proportions for different games. I invite you to think how does your game (or a game you like) does it and post it, so we expand this list in the comments