There are different ways of looking at roleplaying games. Presenting such ways is one of the major benefits of rpg theory, in my opinion.
This is the by-now classical Forge theory perspective. Who has the right to establish what in a roleplaying game? Maybe you take turns to say a sentence that is now true, respecting the earlier inputs. Or maybe there are some tokens. Or maybe the game master plays the world and the players their characters.
This was established by Sandra, Jeph and others at Story games. What are the true statements concerning the state of the game, which restrict or determine what will happen next? Maybe it is "no myth" play where only what has been publicly said and accepted is true, or maybe it is klokkverkblorb play with an extensive description of the game world and the game rules that is big enough that nobody really has a handle on all of it. Or maybe a drama game where character motivations are well-defined and established, but we are not so careful about he physical context and where the grocery store lies and how many floors does the library have etc.
Mythic lens or relationships
Discussed by Jay recently on Story games, and by Chris Lehrich and Jay and maybe others, way back on the Forge. What are the interconnections and relationships between various things in play?
"Roll for initiative." is a ritual phrase that indicates combat, but also evokes a certain game mechanical procedure, but also describes what happens in the fiction ("I go to the bar and ask about the guy with silver hair." "Yeah, roll for initiative.").
The game is set in Japan, so tattoos are a sign of Yakuza.
The game was started with "You are standing on the edge of a fiery pit. There is a figure, like a mummy wrapped in rainbows instead of toilet paper, and with black spots for eyes and a white nothingness for mouth, looming over the scene. Then you wake up." Henceforth, rainbows, fiery pits and mummies, and in a darker game, danger or threat, have now been tied together. If there is a pride parade, someone is likely to ask if anyone has been dressed up as a rainbow mummy.
The totality of these interconnections is the meaning of something. (This grandiose statement is probably false, but should point in the right direction.)
All the perspectives above are always viable means of analyzing any play. The benefits of using each vary from game to game.
None, yet. This is not a description of mythic play or the simulationism creative agenda or any other style of play; rather, this is how I understand a perspective that is fruitful for looking at Jay's accounts of play and theory explanations. Also, the notion of there being several perspectives one can take into use or not, depending on context, is useful, even if nothing new.
(Funny fact: It is a very good measure of mathematical skill to see if someone can understand derivative via the formal definition via limits, as the slope of a graph, as a speed of change, as a linear approximation, as a mapping from one function space to another, and so on. There are probably more elementary examples of the same idea, but this is a traditional one in studies of university students. Anyways, having several ways of looking at a thing and being able to change between them seems to be a useful cognitive skill.)