As I am putting forth there are two major ways of looking at a game. The post-structuralist Forge theory seated squarely in critical theory and games as they were understood for about a thousand years up until that point. IOW, as patterns players decipher, at least in part, to accomplish objectives within them. This is why puzzles are basically the same thing as games historically and held in -abashedly- low regard from the other perspective. No one should un-ironically solve a puzzle from that point of view. And games are best designed when quit of that thinking. As well, game rules have been changed to always be agreements between two people rather than patterns of behavior (Laws of the Universe in D&D). So playing Chess on a computer isn't playing Chess at all as now there are no rules players are following with other people. It becomes a fundamentally different act as there is no self-similar pattern that is the game of Chess making play of it basically the same thing. At least, that's the hardline stance.
I'll try to answer from understanding, but you are making some assumptions that I don't really follow and come to some conclusions I definitely don't agree with.
I disagree that a "game" and a "puzzle" are the same thing, but your computer example highlights that every game has, in a particular sense, puzzle elements. Let me deconstruct the "computer chess" situation: I take it you do consider this to be a "game"? If so, so do I. And it contains a puzzle element - but we can argue that all games do. The game element is, well, "chess". This brings a set of assumptions (an 8x8 squared board and 2 sets of 16 pieces of particular types) and a set of rules (one side designated "white" moves first and the sides then take turns moving one piece per turn - generally - with particular pieces allowed only to move in specific ways and so on).
The "puzzle" element is the fact that the computer has been programmed to play chess using a set of heuristics. Trying to identify the "pattern" of those heuristics might be considered part of the game.
The thing is, though, that the "trying to fathom the pattern of the heuristics" is enabled by the fact that
the computer must abide by the rules of the game.
If the computer suddenly starts moving bishops as if they were rooks (a really rather minor deviation from the rules, in the great scheme of things) most would agree that the game was no longer "chess". The rules of the game are what enable the human player to attempt to fathom out the heuristic the computer is using. The rules do not tell the player what the computer
will do, but they do tell them what the computer
may do and what it
may not do.
Even games such as "20 questions" have rules. 20 questions is a guessing game, but there are still fixed rules that both the querents and the respondant must abide by if it is to be a game of 20 questions:
- The querent may ask up to 20 questions of the respondant, after which they must state what they believe the mystery "thing" is; if their statement is correct, they win - if it is not, they lose.
- The respondant must think of one unique "thing" to be guessed - they cannot change it after the first question has been answered. They must answer all questions truthfully to the best of their ability. They must state truthfully whether the querents' final chosen guess is correct or not.
If those rules are not followed, then you are not playing "20 questions".
It seems very much to me that rules perform the same function in RPGs as they do in these games. They tell the players how they can interact with the mystery in order to divine things about it. They state both what might happen and what cannot happen and, as such, form the basis on which the players can understand the game world. In this role, they are essential.
I don't incidentally, think this is any different from what is going on in what is discussed on the Forge as "gamist play".
D&D doesn't have resolution mechanics as the rules are for a massive reality simulation hidden behind a screen. That description is closer the start of the hobby as any of hundreds of computer emulations of near-D&D demonstrate. Players get hooked on the pattern recognition aspect of games and puzzles. And while they don't "win" they certainly can improve enough to call for tournaments.
If D&D has no resolution mechanics then players have no sound basis for interacting with the game whatsoever. If everything is arbitrary then no useful "pattern" can be discerned and no useful purpose is served by "playing the game". Long ago I actually tried playing a game in which there genuinely were no rules known to the player; it was hopeless. Not only did I have no information, I had no basis on which I might conceivably acquire any information. Was I humanoid, amoeboid, quadrupoid or what? I didn't know. Were the "sights" being reported to me correspond with what human eyes might see in the same situation? I could not be sure.
You might
assume a lot of the rules - that "real world physics" applies except where it explicitly doesn't, for example - but (a) those things remain rules nevertheless and (b) they are extremely problematic as rules because everyone's conception of how "real world physics" works is wrong.
Some of the rules - or, more correctly, some parameters used in the rules - may very well be unknown to the players. But the rules themselves must, to be useful, be fixed and will be used to resolve the results of interactions between the fictional characters that the players use as tools to explore the game/puzzle/pattern and the pattern itself. They are the point of contact between the players and the pattern. If there are no rules defining how the players get information about the game world and how it responds to the actions their playing pieces ("characters") take, how can they possibly figure out what the pattern is?
Here is an example. If the players are authors as well as the DM, a player would feel free to make up a fact about the world on the fly during the game and the rest of the group would roll with it. So I could suddenly have a long lost cousin arrive from the north and be sitting in the bar when I walk in.
In all RPGs that I can think of that use such concepts, such introductions are governed by rules and often require the expenditure of player resources. I think this links back to my responses to howandwhy, above: there are rules that define how the player is allowed to interact with the game world. These rules sometimes allow the player to stipulate things that the character couldn't. The difference is really quite subtle; since neither the character nor the game world really exist (except as patterns of thought in the participants' brains) one might say it is hardly any significant difference at all.