Based in a world similar to that of the novel.
You play the role of a square and you have to go through a world of different shapes. The view point will be that similar to the one described in the novel. Put a penny down on a table. When you look at it from above it looks like a circle. As you go lower and lower it looks like an oval until final you are at eyes level with it and it looks like a line. That is what things look like in flat land.
The goal of the game will be to explore avoid Triangles (pointy and deadly). Collect circles (point system) and simply walk around. or something like that.
The different shapes/lines will be represented as different colors. It will be "3d" a quick example shown in this cast:
http://www.screencast.com/users/tomtom1337/folders/Jing/media/f9ecbd38-e47a-4f35-b6c6-23487b8ad51cThings I want to work on first are changing it so as you zoom out and in too close and too far it doesn't ruin the illusion of 3d.