To me it looks like a quad is a group of structures separated from other groups by wider roads (passages).
Another word for quad could be sector.
I agree that's the general idea here. However, they are playing fast and loose with the term quadrant (meaning ¼ of a circle) - the picture shows five spokes in less than half a circle So it's just the name they came up with in the "sci-fi show English" that resembles a block in "reality English""Up" and "over" are standard street directions in the U.S., where many cities have grids of streets that run perpendicular to each other.
"Up" means go up (i.e. along) the street you are currently standing on (away from your current point). After the specified number of blocks (the distance between two intersections is a block) go over (i.e. make a 90 degree turn onto the perpendicular street) and go the number of blocks specified on that street. "Over" doesn't mean "above", it means across, from one side to the other. (Think "from here over to there". From the point where you turned, over to the final point.)
This is the same idea. But instead of measuring in blocks, they are measuring in quads. Even if it's circular, it doesn't matter. You can still go along one street (like the spoke of a wheel) and make a 90 degree turn onto the other street (shaped like an arc) and count the quads (groups of buildings) you pass.