Actually, with these 'catalyst' pads, it should appear to work

I guess it's some kind of polymer — a source of organic carbon.
The aquarium is depleted of energy that could be obtained from the oxidation of organic carbon in food (
Cellular respiration). Fish consume most of this energy (around 80%?), leaving little available for heterotrophic bacteria or archaea to thrive.
If we supplement the system with organic carbon, microbial life will increase in population. Building biomass involves binding nitrates (and phosphates!) into microbial cells. Various sources of organic carbon can be used: vodka, sugar, glycerin, polymers (like tapioca or PCL), commercial products, or DIY alternatives (
Reef Central forum thread). In saltwater systems, a protein skimmer removes most of the excess biomass.
However, the cure can be worse than the disease. A large additional surface area (not just inside a 'magic brick') is required in the filter to accumulate biomass, and this area must be cleaned regularly. Water quality can deteriorate and become unstable, potentially making fish more susceptible to diseases.
I’ve tested this approach myself, and I find it better to use selective nitrate ion-exchange resins (such as Purolite A520E or PA202),
regenerated with salt, to remove nitrates and DOC if you can aquire them in reasonable quantities. Now I just use drip system.
If someone claims they achieved full denitrification to gaseous nitrogen, I would test phosphate levels — there should be plenty of it left!