I always believed that energy isn't created its converted, its the efficiency and the by-product of the conversion that matters.
Very true.
However, we know how much energy can be gotten from burning the hydrogen and how much energy it takes to split the water into hydrogen and oxygen. It takes more energy to split the molecules than you get from the hydrogen.
If there were some catalyst used to reduce the energy to split the molecules, that might help explain it, but there doesn't seem to be any catalyst in these kits.
The internal combustion engine isn't 100% efficient, but adding hydrogen to the gasoline isn't going to suddenly make it more efficient or make either burn with dramatically greater efficiency.
So where does the energy come from to increase the efficiency?
My guess? They are charging up a battery, using the battery to power they splitting of the water in to hydrogen and oxygen, but not recharging the battery. Your system is actually less efficient, but you're ignoring one of the energy sources.