That just makes Gawker look worse. The rant in question was part of the sex tape, but they didn't include it in the original article - it was published later by Gawker as a direct result of him suing them over the sex tape in question. It looked remarkably like retaliation for him suing them over their publication of the sex tape.

It didn't. His racist rant was published by the National Enquirer three years after Gawker leaked his sex tape.

Wait, who and what is this?

The sex tape itself was widely published on the internet, but most publications responded to Hogan's lawyer's C&Ds. Gawker did not, but more importantly, they separately published the fact that an audio tape exists in which Hogan made blatantly racist remarks about the person dating his daughter, which caused sponsors and others to pull away from him. (Though they didn't publish the tape itself, as others did, perhaps ironically.)

This is what's considered to have caused the damage to his career, rather than the fact that he likes sleeping with his friend's wife.