Earlier quoted context omitted.
His stated goal, "deterrence," is the exact thing people talk about when they worry about a chilling effect. The fact that people are applauding because it's someone they disagree with whose ox is getting gored is really disappointing for a community that espouses such strong freedom of speech principles.
If the intended deterrent is simply the cost defending or settling, then you are right, it is no different to a SLAPP suit. However, our legal system holds that even where we have freedom of expression, we still have a responsibility to not invade people's privacy, and not cause them emotional harm. A court found that Gawker didn't act according to those responsibilities, so they owed damages. That's exactly the kind…
"[...] an unusual decision Mr. Bollea’s legal team made: It purposely excluded a claim that would have allowed Gawker’s insurance company to help pay for its defense as well as damages."
That speaks quite loudly to the intent of the deterrent, otherwise they wouldn't be concerned who was paying, since insurance company money is just as green as Gawker's.