(This is a second take on an earlier post. This one, hopefully, is a bit more useful. It contains a few ideas about how to make a notational system that works. No guarantees, of course.)
The basic idea behind any kind of notation is that you are assuming a standard knowledge, and then applying that knowledge. For example, musical notation assumes you know how to play the instruments. Scientific equations assume you know the math to manipulate them. This is, of course, not entirely true of works which are teaching you to play or manipulate - but even then, they assume you're only trying to learn the algorithm or instrument they are teaching, and already know the stuff they rely on.
The idea that the "notation" of a game needs to somehow be "complete" is ludicrous. In fact, the "artistry" of notations (from novels to sculpture and back around to screenplays) is that they are incomplete. They use what the audience and/or performer will know, and then reach heights unimagined a hundred years ago - because they are standing on a platform built by thousands of people all working in the same direction.
However, unlike music, or screenplays, games are interactive. If they weren't interactive, you could just write them like screenplays. Like most people do now. "The zing jing jumps out at you. (Fight ensues, stats are blah blah.) You continue on to the bibble bobble. (Acquire the Goingiboing Gnarkfark.)"
This isn't suitable. People seem to think games should be linear. Games should not be linear. At least, not all games. The idea that the choices you make choose between utter failure and standard advancement is bad for a lot of reasons, not least that it multiplies the content required to make a game that plays the same length of time as a nonlinear game. (A nonlinear game has much higher replay value.)
Nobody I've seen has figured out a good way to represent the interactivity of games.
This is because people are using the word "interactivity".
Calling games "interactive" is like calling music "sound". Yeah, it's true, but it doesn't mean anything useful. Clipping your toenails is interactive. That doesn't make it a game any more than dropping an egg counts as music.
This is because it is the pattern of interactivity and the pattern of sound that makes games and music games and music. How do you make a pattern of sound? You use an instrument that produces similar sounds but different tones whenever you manipulate it. Then, you can create a wide variety of patterns, all with the same base "noise". By simply writing down the variation in pitch and length, you can record much of the pattern - although the secondary characteristics get lost in the shuffle, because you are writing in a way all musicians, regardless of their instruments, are trained to understand.
How do you make a pattern of interactivity?
Well, one would assume you use something which creates similar interactive experiences when used, but can be manipulated to vary the tone. Like, say, a play loop. For example, the FPS play loop always produces the same basic "tone" of gameplay, but it can be manipulated to produce hard fights or easy fights, fast fights or slow fights, long pauses or difficult maneuvers. Teaching how to "play" these loops - even what loops exist in the first place - might be a bit difficult. The MDA framework provides a nice start for many play loops. It can't represent full games - it can only represent play loops. Hence the need for something which can go further, represent multiple interacting play loops.
There's nothing wrong with having one play loop any more than a song that has only one instrument. However, usually having only one play loop is used for emphasis, like a soloist in a song: patterns only really grow complex when you start mixing multiple play loops.
Like a song which has a guitar, a bass, a keyboard, and a drum, you're going to end up with a much more complex and usually more enjoyable game if you use a variety of game loops, like FPS, stat growth, and linear narrative. The pattern you are representing grows much more diverse and complex.
So, okay, our "instruments" are play loops. And you are expected to know how to "play" them. If you can't "play" an FPS "instrument" to program a game experience, stay away from scores that include FPS instruments - or get another person to join your band. Or, like someone who can't play guitar but can play a keyboard, get yourself something you understand that can fake the instrument passably well.
Now the critical part is representing the interactivity. To some extent, this is actually easier than it seems, because nearly all games use the standard "pattern repeat repeat repeat variance" method of play. The simplest example would be the steady increase in speed throughout Tetris: it's always the same pattern of play, but at an increased speed.
It's true in all games. Each character has a "refrain" they play whenever you interact with them. They are goodhearted scamps or foulhearted skanks. They are brutal warriors or terrified victims.
This extends throughout. The enemies follow the same refrains: the guys with shotguns always play this way, the guys with autocannons play that way. Even - and here's the hard part - even the level layouts and placement of supplies has repeating refrains. In Doom III, you could always tell exactly when you would be attacked, and you always knew exactly when you would get more health and ammo - except in a very few cases.
These patterns, these "refrains", are the game proper. But the exceptions are often what makes or breaks a game. Anyone who plays blues can tell you, the refrain doesn't have to change, because the part it supports - the variations - are endless.
Of course, you need a good refrain. That's why blues musicians tend to stick with the few standard refrains, and rock tends to have a few standard drum beats.
So there would be two "parts" to writing down a game design in this way. Writing the refrains, and then writing their exceptions/collusions. Like music, the refrain determines not only the feel of the game, but also its genre. Which play loop instruments you use in what ways... that's important.
How does this write interactivity?
Well, the refrain is something which progresses without exception. It always goes "buh-wheee-o-whee-wheat", then you can sing about how your woman left you. In the same way, games will always have the same "feel" to them, even if the exact path of the player is up to question. The player will always fight zombie-type monsters here, fire-type monsters here. The player power-ups will always be located after boss fights. The player will always have so many enemy encounters after powering up before enemies power up to match. Maybe fights during the refrain will always go "easy-easy-hard-medium". Or "long range, medium range, long range, short range". Lots of level designers do this by accident, never even realizing they are doing so. See Doom III for an example. :)
Refrains can be anything. They are one or more instruments that play a recognizable "tune" that sets the game's feel.
Now, I can't keep calling them "refrains", or at least I shouldn't, because "refrain" means something very specific in music terminology, and I'm not using it the same way. These patterns in the game - depending on the size of the game, there's often dozens or hundreds of "refrains". A game like Tetris has only one, but a game like, say, Halo, would have a symphony-sized ream of them.
This doesn't seem so different from writing little "pieces of level", does it? You say, "He'll run into fire guys here. They'll be mostly long-range, except a few panicky melee fights. There won't be much healing." That's a refrain. Except the refrain is a much more elegant way of jotting it down, because it refers to the intrinsic but unstated reward and challenge structure. For example:
This could represent the situation I just talked about, with the lines representing long range fighting, short range fighting, fire guys, healing, and ammo. "Played" in your mind (or even on a keyboard, if you like), there is a definite syncopation and rhythm which defines this part of the game.
This represents "first tier" interactivity. It represents play, but not as play actually would be. For example, what happens if the player decides to turn back and explore the level for fifteen minutes between some encounters? The rhythm is suddenly very different. This can actually make a huge difference if you're in a game with something time-related happening. For example, if you heal over time.
In short, it doesn't represent how play loops change, it represents how play loops DON'T change. It represents the part of the game which remains constant.
How can it represent true interactivity? How can it represent a live AI squad roaming the level looking for you? How can it represent the other player stealing health power-ups he doesn't need?
It can't. That's jazz. The designer knows his duty: his duty is to have the play loops form this refrain (and a long list of other refrains, presumably). How he handles the loose ends depends on how he "plays" the design of the game.
Can you codify this into something simple? Not that I can see. I can see putting in "bars" to represent where significant breaks in play can happen, or little slides for where things lead directly from one to the other, but I don't see how you can demonstrate what is functionally 7+ dimensional space on a 2D display.
Instead, you represent the important parts. Like the way you take a photograph instead of sculpting a full duplicate of the scene.
Do I think this is "the" way? No. But it can represent the primary play loop patterns, reward/risk situations, "mood", expectation... it's better than the others I've seen so far at large-grain game depiction. This score has the high score. :)
It's a start.