Note: for the purposes of this discussion, I think the G part is important. That is, it should still be a game (as opposed to a simple storytelling exercise) so there must SOME rules and something that looks like success or failure (although those concepts are fuzzy in RPGs). But with that in mind, what is the bare minimum level of rules you need to feel like you are playing a TTRPG?
Thought I'd analyze this a bit (and stop in to see if anyone else provided an actual number of rules). This quoted part is important. Games have rules. In those rules, there are some nebulous requirements. Let's take a stab...
Role-playing: gotta have a rule about creating or being a character, even if prescribed.
Competition: two opposing sides seems to be a minimum. Interestingly, a win-condition hasn't been needed since the RPG evolved from the war game.
Randomness: surprisingly, this isn't as necessary as I'd thought. The ideas that come out of a human head are all the RNG that a gamer
needs.
Wants, however...
Goal: this doesn't have to be a win condition - end of game. But it's something for which to play; it moves the competitors forward (see my rule #1 earlier in the thread). It's the goal that requires...
Navigating the competition:
how do the competitors compete? Whatever the method, it'll probably need a rule.
Did I miss anything?
Minimalist: Basically, a core mechanic. You don't need anything more than the barest of bones.
Whenever D&D invokes "core mechanic," it's talking about a few different ideas: rolling a d20, a difficulty class (DC), two types of player, and the results. Assuming that's the "core mechanic" above, this minimalist option refers to about four different rules. There's still a character/role-playing requirement (which of the two types of player are playing a character) and a goal requirement (why are we doing this). I'd put Minimalist at 6 rules, minimum.
Light: Core mechanics are great, but you need a little more than that: a couple subsystems to cover broad topics, maybe a short codified list of character and/or NPC abilities, etc..
I see the core mechanic has multiplied (/snark). And subsystems are popping up, which would need to be at least 2 rules each (otherwise they're not "systems," they're just rules). I also like the term "rules modules." Anyway, I think we can assume that a subsystem probably shouldn't be much shorter than the core mechanic above (4 rules), so I'll say 4 rules times a core mechanic and two subsystems is 12 rules, plus the 2 required rules from above, is 14 rules. Lists are here too, and while they make a system beefier, I don't see them as rules so much as things you can do with the rules. Lists can shrink and grow, but that doesn't change how you play the game. So I might expect Lists to be more of a Moderate-sized feature, but something simple for Light-sized games isn't bad.
Getting more concrete from here just seems to involve page counts. Or numbers of book-covers...?