In my introduction, I said that I would be discussing a genreless theory of design. Why genreless? Why is genre so bad?
Genre is a fine thing. In fact, genre, more than anything, informs game design. Each genre carries with it certain specific game design ideals that define that genre, and members of a genre are free to implement game design within this specific context.
There are two problems with genre. From an analyst perspective, genre is useless information. If you're analysing a game design, the dictates of its genre must be part of that analysis in order for it to be considered complete.
The other problem is that genre is fundamentally limitting to game designer freedom. Let's look at arcade game design pre-Donkey Kong.
You had a number of genres. Shooters (Defender, Galaga, etc), Pong-a-likes, and a few others.
Then, some nutball came up with the idea of a platformer, Donkey Kong, a game that looks very different from anything else in the time period. Your main character is a human (cartoon-ish though it may be). It involves maneuvering the character through a hazardous environment, often with few abilities to actually kill anything. That was heresy in those days, for the most part.
When it comes right down to it, if your first idea with a game is based on known genres, you have less of a chance to make a game that is unique.
Now, it is not a bad thing at all to follow the beaten path. Not only is it less likely to turn people off from playing it, it is more likely to actually work, because you actually know how the genre works. Also, you can make a genre entry stand out from the crowd by adding new gameplay, where it meshes well with the genre. Or you can correct flaws in other entries in the genre.
From an economic perspective (and there is nothing I hate more when dealing with game design than dealing with how well the game might sell), one needs to understand an unpleasant reality about the genre lifecycle. There's an article* on Lost Garden on the subject that gives it a decent treatment.
Even so, the basic fact is that the most innovative games tend to be seen as those of completely new genres. And it's hard to dispute that: Donkey Kong, the great grandfather of platformers, was a watershed moment in the evolution of videogames.
If you're going to profer a valid theory of design, like good scientific theories, they should actually predict something. They can't just tell you what works now; they have to tell you what will work tomorrow, and why a game to be invented 100 years from now will work.
* I don't like this article's inference that the lifecycle of a genre ends at niche/death status. I don't think there's nearly enough evidence to say this, with only ~30 years of history for videogaming. Especially since most of that history has driven the adoption of new genres by technology; it's hard to go back and play, let alone make, older-tech games, particularly when you have to compete against more advanced games. I think there's great potential for "genre mining"; that is, going back to some of those older genres, giving them an appropriate coat of paint, and making games using modern game design ideals with them. I believe that a genre can be reinvigorated after an appropriate length of time has past, much like the modern movie epic genre was reinvigorated by Braveheart.