Re: How do you start designing a game?
My process lately is: I think of something that I find enjoyable, an experience or activity, and then try to think of how you could make a video game that captures that.
A game I'm working on right now is essentially PONG, but played with a group of people, and as people get eliminated they become spectators and watch/comment on the remaining matches.
I realized that I enjoyed playing video games more when people were watching me, and so tried to make a game that revolved around it.
Your example approaches all seem to be talking about the plot of a story, rather than game mechanics. If you used those approaches, you could come up with a story, but you still wouldn't have a game. At that point you'd need to invent the mechanics of your game.
I'm of the opinion that games do better when they aren't trying to tell a specific story. Other artforms do that better. I think games are best when you create a set of rules, and let players just go to town with it. If you have interesting rules, then players will begin to create their own stories by doing interesting/meaningful things in the game.
For example, Halo had really deep mechanics that allowed for all kinds of awesome stuff to happen in a match. Specifically, the multiplayer: Epic rocket launcher shots, harrowing escapes in Capture the Flag, huge killing sprees, etc. And it was always a result of player choice - it wasn't a scripted event written by the developers. I think because the players could feel like they had complete ownership of what happened in those matches, it was more meaningful to them. Just like some crappy Flash game has more significance to its creator than an epic AAA blockbuster, simple stories can be more meaningful than epic sci-fi arcs if you feel like you contributed in a real sense to them. Every moment playing Halo with my friends where something totally awesome happens that has everyone yelling, that's the players creating their own stories.