I don't quite follow the logic.
Gawker outed Thiel - not illegal, he didn't sue, but they made an enemy.
Gawker published Hulk Hogan's sex tape - this was illegal, but they assumed he wouldn't be able to afford to sue them.
Thiel backed Hogan to sue Gawker and won - Hogan got his justice, Thiel destroyed his enemy.
Lawsuits are expensive - this is the problem/weapon.
Yes, Apple could back 1000s of libel cases against El Reg, and this would be bad - but this isn't what happened here. Thiel didn't back 1000s of cases against Gawker to grind them down with legal costs (and you'd hope if he did, punitive costs/counter-suits would be awarded against him for frivolous and baseless actions - although sadly not normally the case).
The 'expensive lawsuit' problem in this case was that Gawker felt they could get away with illegally publishing the sex tape, as Hulk wouldn't be able to afford risking legal action.
i.e. They wouldn't have published a sex-tape of Thiel, as they knew he was rich enough to sue. They published it as they thought they had more funds available than Hogan - and came a cropper as they were wrong.