Yes another Garrosh thread. Anyways, a lot of people here are speculating Garrosh is going to break off and go evil again. I mean, it's unlikely they let him survive the siege just to be killed later on in a trial. But, why would he be so eager for revenge?
Look at his face in the cinematic. He's crushed. He can't even muster up the will to say anything. Garrosh, the proud Orc Warrior, has been defeated in combat, and spared the glory of death. The last part is very important. Garrosh lives off 'Victory or Death'; He led the Horde on that ideal alone. But he hasn't been given that, the honourable death every Orc aspires to have.
That isn't the worst of it, however, Garrosh has done exactly what he was afraid he would do. He turned into his father, leading the Orcs into darkness, giving into a power greater than his own. In Nagrand, he was worried of doing just that, he didn't want to lead the Mag'har because he knew he would do just as his father had done, and bring them to corruption.
Living right now is a far worth punishment to him than death. He has to go on knowing he was weak enough to lose himself, and that he doesn't have what it takes to be a leader. He's going to be just like he was in Nagrand. And that's where Anduin comes in. Anduin still forgives Garrosh, and believes he has a chance to prove himself. Thrall failed in Nagrand because he didn't warn Garrosh of the temptations of power. Now that he knows of it, how would he react to a human prince, who he himself has tried to kill, reaching out to him and trying to help?
As much as I hate him, this is Garrosh's chance at becoming at actual good character.