According to both the san francisco chronicle article "free speech versus kids and violent video games" and the huffington post report on the supreme court ruling, the california law regulating the sale of violent video games to children was overturned for all of the following reasons except

there was no research showing a connection between violent video games and psychological harm to young people
there is no tradition in the united states of restricting children’s access to depictions of violence
the supreme court has upheld laws keeping minors from buying or having access to p*rnography, alcohol, and tobacco
governments do not have the power to "restrict the ideas to which children may be exposed."