In this case, the federal judge supports total incorporation. This is evident from his ruling that sides with the newspapers. By making this ruling, the judge is establishing the precedent that the rights guaranteed in the US Constitution apply to all states.
The Due Process clause of the 14th amendment states that the government cannot deprive individuals of "life, liberty, or property" without due process of law. This means that citizens must have the ability to take this ruling to court while being represented by legal counsel. In this scenario, the newspapers are arguing that they did not have a fair chance to protect themselves against this new state law. This law was forced on them and is hurting their ability to pursue "liberty."