I don't see the difference...
They hold the same stance in both situations... they refuse to take down the images/video until a court orders them to
If you could read, you would see that a court did order them to take down the images of Hulk Hogan. Gawker refused to obey the court order. They say they love to see famous men naked because it's something they're not supposed to see, and it is satisfying.
At the same time, Gawker says that sites should remove nude pictures of women even without court orders, because they believe that being a woman grants a person automatic ownership of all images of her own body, and that her privacy should be respected. They don't even name the site hosting the pictures of Jennifer Lawrence, because people looking at naked women is
wrong. Gawker refused to host those pictures on their own sites, despite the public interest being hundreds of times greater than the interest in Hulk Hogan's pictures.
When it's a man, Gawker describes it as a shameful and dirty video of him "fucking", and notes that it's not even sexy despite his "ostensibly" fit body.
When it's a woman, it's assumed without evidence that an evil "hacker" has "leaked" these sensitive, private photos, which feature "some of the most famous women in the world" who should be revered and respected. And plus, maybe these photos aren't even real! But they should still take them down! There is no vulgar mention of "rubbing their pussies" or "bending over and showing their assholes" or "they aren't even sexy like celebrities are supposed to be".
So their stances are the complete opposite in the two similar situations, with the only obvious difference being the gender of the victims.