That article describes using an on-board electrolysis cell to generate hydrogen and oxygen which is then burned in the engine. Considering that the exhaust is simply water, you could connect the exhaust to the water storage tank and never have to refuel. In other words, it's a perpetual motion machine.
Say an engine requires 100 BTU/second of energy to operate. Assuming the electrolysis cell is 100% efficient, we put in 100 BTU of energy to break the water into O2 and H2. At best, we can recover 100 BTU of energy when the Oxygen+Hydrogen are burned. So we burn the O2+H2 mixture in the engine. Now, the internal combustion engine is notoriously inefficient, loosing about 80% of the energy in the fuel as heat. So, at the crankshaft, we now only have 20 BTU of energy available to move the vehicle and generate more hydrogen.
Electrolysis, or any of the other methods of splitting water into H2 and O2, is not a way to create energy. All those methods do is convert energy from one form to another, usually electrical to chemical. Because the process is never 100% efficient, performing that process on the vehicle won't work; the engine will not be able to power itself, let alone move the vehicle.