I'm sorry, but I think a large part of why you think it's a poor fit is because it doesn't illustrate your point.
Not sure I follow you. My point is that the poker game you're talking about is a metagame for poker. It's like claiming that character optimization is part of D&D. it is, and it isn't. It's an extra game that only exists when the first game does, and it's focused on gaming the underlying game. I think it's an excellent distinction to note the game presented from a metagame that exists on top of it. And that's what you're illustrating with your poker example.
It's a good point. Metagames almost always exist. But, I don't think it correlates to discussing how games function within their rulesets. It's, well, extra.
Labeling some parts of a game the "metagame", correctly or incorrectly doesn't make them any less important parts of the game. You can label the most important parts of many games ie; social deduction games, trading games, alliance games, calling plays in football, a pitcher reading a batter, etc. etc.; "metagame" but that more often that not just leads to a lack of understanding of what those games are and how the rules influence that.
I disagree. I think noting something is a game about playing a game is a pretty big distinction from discussing how a game plays by itself. As I said, I can play poker without bluffing -- this is pretty much what happens when you play against a computer. Certainly we can't claim that my inability to read the computer or bluff it means I'm not playing poker. The meta-level of games, where you play a game on top of the game, is very interesting, but, again, not actually part of the underlying game. Poker is separate from bluffing, but bluffing in poker requires poker to exist.
Adding more rules about those things DOESN'T mean the game will have more focus on those things, or that those things will function in a more satisfactory way.
I'd disagree on the first, somewhat, and agree strongly on the second.
Re, the first point, having robust rules for a thing usually will mean that a game will focus on that thing over an area that has weak or no rules. Take D&D. Granted, you can have a session that focuses on roleplaying, or shopping, or building a castle, but how much occurs how quickly there? Combat slows down and gets granular whenever it shows up in D&D -- it demands more focus for resolutions, and resolutions are always very precise and complete. D&D directs focus to the combat rules across lots of segements, from character build, to equipment, to strategic play, to tactical play in the combat engine. There's even the combat swoop, where you shift from the more freeform exploration/social pillars to the combat engine via the initiative roll, which particularizes timing and structure in a way the other pillars usually do not.
Does this always hold? No, it's general statement, not an absolute one. If a game system invests in robust rules to adjudicate an area of play, though, that area is usually going to be a focus for play, unless there's a strong effort to thwart this and use the system in other ways. That's something you can do, but then the system fights you a bit by not providing the robust systems while you avoid it's most robust systems.
On the second party, absolutely. More rules does not mean better rules. Or better outcomes. Heck, look at Palladium systems -- lots of rules, not great outcomes. You have to hack that system a bit to get it to even work.
To which the response is likely "Sure, that is easily observed, but ttrpgs are different." However, I am not the first one to make the observation that the same thing is true. Having more rules for things doesn't mean the game having will have more of that thing occur, or that it will be more satisfactory when it does.
Goodness, no. I have no idea why anyone would assume that.
And you can't, unless you specifically choose a definition of roleplaying that means you can.
Agreed. Usually when people do choose those definitions, though, it's pretty clear they're either engaged in a bit of one-true-wayism or just trying to derail the discussion. I do think that most systems leave roleplaying as an exercise for the players to develop rather than a place to provide operationalization. Just some light constraints and incentives and a bit of authority granting and that's it. 5e does this through the background system (which is an operationalization with incentives), the usual genre constraints, and authorities to the player for action declaration and the GM for resolution. This is enough, though, to get to roleplaying, and open enough to accommodate a number of definitions and styles of roleplaying.