The shower works on similar principles to a Dyson vacuum cleaner, using filters and hydro cyclones, installed behind the shower unit, to clean the recycled water and reheat it to the desired temperature.
Now, it's going to be using some energy to do the filtering, but at the same time, it might also save energy. How come? Well, the major energy input into a shower in this country is heating the water from cold water temperatures. Since the water it's recycling will presumably be somewhat warmer than that (it was just running down your back!), that should make up for it. I'd be interested to see a full energy budget for it.