There are a lot of theories out there as to how to talk about games. Most people seem to want a formal vocabulary for discussing the aspects of game design.
I disagree strongly. A formal language? Formalizing what? We don't know anything, so how can we formalize it?
We're inventing all these languages that divide up a game into such tasty-sounding pieces, but based on what? To what end?
For example, I like MDA - mechanics, dynamics, and aesthetics as posed Marc LeBlanc. It's not the first thing he's posed, it probably won't be the last, and it's a fun brain exercise.
But people are taking it to heart, treating it like it's a formal, scientific approach.
It's just a general way of thinking about games.
This happens a lot: someone posts something that has categories and subdivisions and people say, "oh! It's internally consistent! It must be right!"
They are arguably formal, but don't mistake "formal" for "right". Astrology is also formal.
Thought exercises are grand things. They're just about all I do. But don't mistake them for solutions. We don't know the first thing about games: how could we accurately represent them?
Someday, thought experiments like these may lead us to stronger knowledge. Maybe, someday, we'll be able to have a formal grammar that isn't just voodoo dressed in a tux.
But not today.