Actually, I think their idea might be better than a screened floor. They have a small drain installed into the tile floor, and are then placing the cage on top of their homemade 55 gallon stand. You can see the rubbermaid containers directly below the drains. Excellent design.
I am currently planning out Ezhno's adult cage and these plans will help. I think I will definitely use their stand design.
You might get a little standing water. I can think of some ways around that though. You could install multiple drains. Even better, install some kind of slightly angled wedge around the inside bottom of the cage. Then nail\staple the tile to this angled wedge. All the water would flow towards the center drain As long as the angle is slight enough, plants should have no problem staying in place.
Some advantages I see in using plastic tile:
Plastic tile is much easier to clean than screen.
Would be easier to setup your water collection. Using a screen bottom means your water collection container must cover the full size of the cage floor.
Feeders that fall to the bottom will not fall through the screen.