The car does not run on water. The article you link says quite clearly that "The car runs on acetylene gas".
Acetylene is an explosive gas that is used for welding, and before the invention of electric lamps it was used for lighting. It is produced from the reaction of calcium carbide and water, as follows:
CaC2 \+ 2H2O → Ca(OH)2 \+ C2H2
The problem is that, while water is cheap, CaC2 is not. It is normally made from methane - which would be a better and cheaper fuel. Converting it to Calcium Carbide is done by partial combustion, so some of the energy available in methane is lost.
For more information on acetylene, see the Wikipedia article.