I don't mean to answer my own question, but trying to explain what I meant ended up so long that I might as well have put it as an answer. This is the technique I use currently, but I'm hoping someone with more experience in the industry can give a better answer.
Elevator pitch: Describe what the game is about in as few words as possible. Describe the genre and target market. What makes it fun and stand out from other games?
Game philosophy: What are features that necessarily have to be in the game to make it feel as it is? What 'feel' would players look for in sequels of the game?
Some examples would be "Can be played 5 minutes a day", "Players should be encouraged to cooperate but the mechanics can be used to settle conflicts", or "Pace must be suited to playing on online forums and email."
Core mechanics: Based on the philosophy, what technical components are vital to the game? On a very tight budget, which ones can be dropped? What code and programming languages are available that can do this right now and do they do the job well enough?
This part should make perfectly clear the technical and design challenges in creating the game, and cut out on the feature bloat.
Simplest implementation: The absolute fastest way to implement the concept and core mechanics. Can it be modded into an existing game? Which components need to be prototyped, which are tried and tested?
Sample of play: Similar to Dwarf Fortress's Power Goals or Stories. This is a brief rant about how cool the game would feel like. With a good enough game idea, it is inevitable to rant somewhere when describing the game, and this is left as an appendix to capture what inspired the game.