Kinda. Let me go back and use a few different examples that might help make this more easy-to-understand.
Going back to the FKR idea, imagine the most free-wheeling FKR game ever. Say, Perfected.
We both roll dice. If you roll high, your view of reality prevails. If I roll high, my view of reality prevails. If we're close, we negotiate.
Those are the rules of the game. That's it. I would say that this game has almost nothing to say about the second-order design, and, in fact, the diversity of play that would spring forth from the rules (the first-order design) is pretty obvious.
Without getting into the "what even is a game?" discourse, I think I understand the proposal in this specific case just fine. This is just stripped down cooperative storytelling, there is no resolution of actions that isn't established by the players themselves. I can imagine some secondary procedures that might emerge (say, maybe I start a description unfinished, with the intent that the other player will fill in what comes next), but there isn't a ton of space for more rules. I'd quibble about whether this is a comparable class of activity to what I'm generally doing when I play a TTRPG, but I think that about a lot of stuff that lives under the broad umbrella.
So this is the area I'm prodding at. What's different, really, about moving the design questions away from the people publishing sourcebooks, to the person at the table? There's different people doing the work in both cases and in different environments, but the process, and any insights into how design might work still hold in both environments. I could take a system that leaves a lot of this in the air and start applying my own sensibilities, and whatever I produce could essentially be republished as a sourcebook of new rules.On other hand, take D&D. As I keep noting, there are areas in which D&D has explicitly not required a given approach. ToTM or Theater of the Mind (or hybrid) is the easiest example. There, the designers of the game are punting on something that, for most games, would be fundamental to the play.
But I wouldn't say that there is anything inconsistent about it. Most games from the 70s, as I've noted before, arose out of consistent second-order design as applied to OD&D. Even the earliest superhero game was just the DM's notes from an OD&D campaign that travelled between worlds.
I don't know that I see a virtue in intentionally pushing that work down the line from your initial product, so I'm looking for a trait that separates doing the design work there, from doing it before the first book comes out that creates one. I might just be looking in the wrong place. I'm trying to find a way to understand praise/critique of rules that push for second-order design, because so much of it seems to be built on future, second-order designs that don't actually exist yet, or aren't available to anyone else in the discussion to review.