Ok, the side yard project is a vegetated swale with check dams rather than a true rain garden. Side yards, even if they are flat, do not typically have the space to store all the rain water from the roofs. In this case the water is damed up in the channel that runs down the slope between the houses. The water that does infiltrate helps nurish the plants (they can tolerate the momentary ponding) and then any remaining water is let out more slowly than it would have occured otherwise.
The other idea this project tests is vertical storage. Basically taking draintile to create a vertical column where water can be stored. It increases the capacity to store water while increasing the infiltration. After attempting this, I've realized one really needs a deep hole for this to work efficiently. Mine are only a foot and a half deep. It is still a great idea for small spaces.