Well the the concept is that the algae will use nitrogen in some form, preferably ammonia(they feed off nitrates as well) , along with phosphates and some form of carbon, obviously using photosynthisis to grow. To make the algae grow very fast, so fast that all the nitrogenic waste will be used as fast as it is being produced, very bright lights 400w to 1000w are suspended over very shallow trays of water. In these trays are mesh screens at which water is passed over them in a wave motion, this is acheived by using Dr Adey's patented (wave) dump bucket. This is a very rough explanation, if anyone wants to know additional information, merits or drawbacks , just let me know.
It seems pretty expensive to run an algae scrubber - 2400 watts!! I guess the advantage is complete nitrogen removal, though. By comparison, you could run two or three fluidized bed filters with probably just one 20 watt pump for complete biological filtration of a tank that size. But you'd have to depend on sufficient water changes to avoid nitrate build up.
I only bring it up because it gives me an opportunity to frett over how to filter a tank I wish I had.
The plants/algae in your scrubber will consume ammonia first. It is the simplist form of nitrogen for the plant to use. Nitrates and nitrites have to be broken down into ammonia by the plant in order for the plant to use it.
It is definately a very expensive way to filter. But the benifits far outway the expense, one is that oxygen is always at supersaturation levels when the lights are on and Co2 levels are usually below 0.9ppm . I know that ammonia is much more easily utilized than nitrates or nitrites, I have done extensive study in this area. And the site you showed is very interesting. And as you say I could probably filter the tank for half the cost, but with that way of filtering and without plant life in the tank, it would produce less than ideal conditions for the fish.