It is certainly freedom of the press, and freedom of speech; but ultimately serves no public purpose. It's just also mean and ridiculous.
Freedoms of this nature must be protected regardless of the context. Gawker's unethical behaviour accross the network, from outing comfortably closeted gay people to failing to disclose obvious bias, is awful; but should not be forbidden. The cure is worse than the illness. My apologies to Matt Drudge if it seems like I'm making light of the action as intellectual pornography.