From what I've seen on that website, the problem is a lack of understanding of thermodynamics on the part of the person who wrote the web text describing the device. Either that, or they know thermodynamics perfectly well but hope that you don't and that they can part you from your money as a result of your ignorance.
Splitting water into hydrogen and oxygen isn't a "free" process, regardless how you accomplish it. The products have a higher net internal energy than the starting material (water), and that energy has to come from somewhere. Think about it: that's why you get (heat) energy back when you re-combine hydrogen and oxygen to make water- it's why hydrogen is useful as a "fuel". The energy to split water can be provided in the form of light (i.e. for photocatalytic hydrolysis), heat (i.e. for thermal/catalytic water decomposition in solar furnaces), chemical internal energy (i.e. by adding sodium metal to water to produce hydrogen and sodium hydroxide), electricity (i.e. electrolysis), but it must come from somewhere.
If you use electrolysis, the source of the energy is electricity, which is basically "work on tap"- it can be readily converted directly to work, and hence is "high-grade" expensive energy. It's an easy process to accomplish physically if you don't care about efficiency: simply throw a 9V battery into some sodium bicarbonate solution and you'll start to make hydrogen- but it's not "free" hydrogen by any stretch of the imagination. Using electricity to produce a chemical product (hydrogen/oxygen) whose energy can only be indirectly re-converted back to work via an intermediate process is far from sensible unless the electricity in question is essentially "free".
