Because this is a civil case, that's why. The government has does nothing to Gawker. No one has been censored, illegally detained, or made to vanish. That is what free speech is about: ensuring the government cannot censor or retaliate against you for publishing an piece of work that criticizes the government.

In civil cases, freedom of speech does not cover defamation of character (libel and slander). I think publishing someone's sex tape could definitely harm their reputation, which is what free speech does NOT protect.

Relevant XKCD: https://xkcd.com/1357/