The prefilter is necessary or the media will clog and you will not have the necessary carbon source. The 3166 feeds a very small amount of filtered water to the biohydroreactor, the low flow allows and anoxic zone to develop where nitrates are broken down but this also requires a carbon source and the debris from the filter cartridge (basically a tea because the solids remain trapped) provides the carbon source. You don't necessarily need the 3166, you could use a Tunze powerhead (non Stream) with a Pot Filter 820 and a flow diverter to feed the unit.
I should note that this method is not absolute like adding carbon sources like Vodka. It depends on the make up of the aquarium and some aquariums are too carbon deficient for this method to work but that is fairly uncommon.