There's no real public information about what goes into this additive.
However, based on the claims and dosage (which are very similar among a wide range of additives) it is likely to be an organometallic agent of some description - most likely ferrocene or a derivative, or possibly something like ferrous picrate.
Based on the advertising blurb the gasoline version is a derivative of the original bunker fuel and diesel additive - so it's likely a general purpose additive containing metal deactivators (fuel stabilisers), a biocide, a water dispersant, high pressure lubrication additives as well as the organometallic catalyst.
Organometallic catalysts were widely used as octane boosters in gasoline, until car manufacturers started complaining about shortened life of emissions systems components (which was costing them big, given the federal emissions warranty requirements). The "top tier" gasoline specification which is developed as a consortium of car manufacturers and oil companies specifically prohibits organometallics in "top tier" gasoline. These days, top tier gasoline achieves high octane ratings by the use of aromatics (xylene/toluene and derivatives) and ethanol rather than organometallics. In terms of the test, as the substance likely does operate as an octane booster, it could well have increased the power output. I would really have liked to see an OBD2 log showing ignition timing, but no one has ever actually done this.
For what it's worth, I used a similar ferrocene based additive for about 10k miles, in an attempt to decarbonise my lexus because of occasional misfires which are probably due to sticky intake valves - due to the engine design, it's a ridiculous job to get access to the intake valves for inspection and cleaning - so the only viable option was some "liquid wrench". It might have made a difference while I used it, but I don't really know - it did get a heck of a lot worse in the 10k miles after I stopped - so, I've just ordered another bottle and I'll give it another go over the next 10k miles.
That said, I checked the plugs in the engine after I finished the bottle of additive, and they were completely brown due to iron oxide deposits from the ferrocene.
As to carbon deposits, organometallics are widely used in diesel and heavy fuel oil engines because they reduce soot production. Ferrocene derivatives are used as DPF assist agents. Many cars come from the factory with a quart or so of organometallic catalyst concentrate a small dose of which is dispensed into fuel tank every time you fill up at the pump. This reduces the soot burden on the DPF and lowers the regeneration temperature of the filter, reducing the need for fuel or valve timing assisted regeneration.