That is a super cool way of thinking about it! I, too, am unsure if these specific boxes are useful categorization tools--but then, I feel like I've grown out of the need for essentialist, bright-line definitions of such things. It's a substantial enough epiphany to realize that people can look like they're playing the same game, but making a mess of things due to incompatible expectations or desires re: what that game is supposed to do.

Ultimately, a taxonomy of creative agendas or whatever is only going to help you with the theory side of things, not the practice. (That the word "theory" comes up again and again to the point of semantic saturation in these contexts makes sense!) I feel like I need much more help with the "so what do I do about it?" question. Once I've identified that different players at the table have different expectations about the thing we're going to build, how can I facilitate their getting back into a harmonious understanding? Or how can I get everyone on the same page prior to game start? The aptly named Same Page Tool may be one option!