Am I reading this correctly? He could have waited them out a little longer and walked free, but they would still be pursuing him in any future country?

probably not, they got away with torturing him keeping him imprisoned essentially indefinitely.

It make me sick to think there are people out there who perpetuated and actively worked to destroy this man's life.

They might lose an extradition fight, but the extradition fight could stretch on for who knows how long leaving him in jail; still a win for the U.S. Taking the deal lets him out of jail.