Those marriages are not recognized by state law and are therefore not valid.
The Governor does not have to "do" anything about them anymore than our State Governor had to "do" anything about the doggie wedding my kids once conducted "marrying" our neutered male dog to the spayed female dog belonging to another neighborhood kid.
You must have missed this from the article:
The US city of San Francisco has become the first civil authority in the United States to officially marry gay couples in open defiance of laws banning the practice. The city, under the orders of new liberal Mayor Gavin Newsom, officially married at least 15 gay couples and issued marriage licences to around a dozen others.