Yeah, turf roof, green roof, living roof, etc., are all variations on a theme.
I wasn't involved in the roofing stage of the build, so don't have any pics of it. But you could have a look at
his journal. There are a few details and pics there.
I don't think there is anything other than a slope on the roof towards the gutter to deal with rain. It's not in any way intended to be a method of water collection - rain that is not absorbed by the plants/soil will simply be runoff into whatever - a water butt possibly, or just into the ground. In fact he's anticipating having to add water at times, and has laid a 'leaky pipe' irrigation system in it.
There's another green roof in mid-construction
here. Again, I've not had much to do with the roofing on this one, and I'm not sure how he's dealing with rain and runoff on it. The roof just has a simple slope to it.
P.S... Bug caught on fire
Oops! You weren't meant to barbeque it.