EzekielRaiden
Follower of the Way
When used in this hyphenated fashion, it is a jargon term I've invented, since I don't personally care for the term "creative agenda." A "game-purpose" is something a person making a roleplaying game sets as a (perhaps the) goal of their design, what play is "for" in that game. Thus, things that can't be strictly "designed for" (such as effortlessness) may still be something worth having, indeed may be something a designer absolutely should strive for, but they aren't a "game-purpose" in this sense.I'm not quite following this. If it is something a player desires from their play and aims for, can you clarify how it is not their purpose? Perhaps there is a semantic issue clouding this, as desire is listed among synonyms for purpose. Can it be restated in different language?
It seems that citing it isn't particularly productive, but I've mentioned Aristotle's causal theory for a reason. A "game-purpose" is like a "tool-purpose" or a "software-purpose." It is both an ideal toward which the tool, game, or purpose bends, and (because games, tools, and software must be used to do something, otherwise they are inert) also the actions that will need to be taken to give life to this goal.
Perhaps "game-design-purpose" clarifies it? This is about design, which is distinct from use, even though use necessarily* follows in part from design. What are games made for doing? Which is distinct from player motives. A "game-(design-)purpose" is the overall goal of the roleplaying design effort, the terms (Score, Conceit, etc.) of play and the process (Achievement, Issues, etc.) of play that produce such a thing. A "player motive" is whatever reason the player may have for choosing to play a given game. Praise or prestige, for example, are (aspects of) "player motives," because it isn't possible to design a game such that praise or prestige will be simply summoned out of the aether by the game itself--these things can only be conferred by other players, due to having played. (As OSP's Red once put it, "There is nothing less cool than someone trying desperately to convince you that they are cool.")
You can, for example, design a Score-and-Achievement game in such a way that the Score is brutally hard, such that few people will have the patience or interest to actually complete it. Poorly-done examples of this in the video game space are sometimes called "Nintendo Hard," though even that requires caveats. (TL;DR: old games had to be small and simple, so brutal difficulty was required to make them last. Today, games are vast and spacious things, so they can have nuanced difficulty.) Well-done games of this type tend to be riotously popular with a narrow slice of the gaming community, see: From Software and their products. Elden Ring appears to have been a sweetspot, just hard enough to still give the "HURT ME PLENTY" fans what they want, but accessible enough to take a solid slice of the wider gaming community.
But even if your game IS brutally hard...there's no guarantee people will receive praise or prestige for their success. Some games become (in)famous for their difficulty, so if you can say you beat them legitimately, you will likely be afforded that public esteem. But some games are just...hard because they're hard, and won't mean much to an outsider. That one game with the jumping square gliding to the right against a techno soundtrack, for example; I can't even remember what it's called, but it was famous once upon a time and that fame has diminished, taking with it most of the praise or prestige for having earned great success (=Achievement) in playing it.
It's not really possible to design a game such that it will get people praise if they play it. We may have skinner boxes, but they're not that effective at psychological manipulation!

Perhaps a better way to phrase some of what I've said: I see my "game-(design-)purposes" as answers to the question, "Why would someone make this roleplaying game?" The different emphasis is important. It is the making, not the playing, that is central to the question; as far as I'm concerned, the motives people have for wanting to play roleplaying games may outnumber the stars, and they're certainly too numerous for me to try to nail them all down. But it isn't just the making in general--it's the making of this specific game. What is its gameplay loop? What is the point of playing this game? And if we can identify what general categories of "the point of playing this game" exist, then we can start asking (which I think you may have already leapt to doing), "How does one make a great game with this point-of-playing-a-game?" Hence why you seem to be very focused on player motives (the things that a well-designed game should account for) and individual design techniques/tools (specific ways in which the designer can pursue the intended design).
*To some extent. Abstract things, like software and games of all stripes, can be heavily, heavily modified, to the point that they go well outside their original design. Mods, or house rules, can be seen as use re-defining design, but that goes well beyond what I'm trying to examine, not least because of how self-referential/meta this can become if you do try to account for ad-hoc systemic redesign to fit player motives.