Ok, it looks like she made the cage liner to fit the bottom first. So she sewed the 3 layers together and ended up with a thick pad, like a comforter.
Then, I think this is probably how she made the sides:
1. She cut 2 pieces 12 inches wide (to go up the 6-inch sides and come back down) and 26 inches long, and 2 pieces 12 inches wide and 40 inches long.
2. She sewed all 4 pieces together along the 12-inch sides, so she ended up with a gigantic long strip of fleece 12 inches wide and 134 inches long. This is the fleece for the sides and it will look sort of like a square.
3. Then you PIN the bottom edge of that long square-shaped strip along the outside edges of your "comforter". It should match up exactly and make sort of a fabric "box" with 12-inch-tall sides and a thick, padded base. Once you've pinned it, you'll see the shape of it very clearly, and it will make sense to you. Sew where you pinned (I'd sew it along the outside edge, so your seams will be touching the coroplast and it will look neater).
4. I'm then assuming you can just drop the whole thing into the cage and fold down the 12-inch sides over the coroplast. She doesn't mention using elastic or anything. I think you will need to kind of tweak it into shape once it's on, as she says she made it slightly smaller than the coroplast, but it should fit very snugly.