Scroll down for the spoilers.
The new Warchief of the the Horde is Vol'jin.
Garrosh is not dead. He is standing trial in Pandaria.
The cinematic is below:
Update 9:20pm EDT:
We are hearing there are two versions of the cinematic. One is what the Alliance sees, the other is what the Horde sees. We're hearing the Horde one is longer. We're researching this and will get you more information as it comes in.
Updated 9:25pm EDT:
Huge Alliance spoilers in the lore dialog after the cinematic:
Replaced the Alliance cinematic with an HD version from our friend AdriaCraft
. The Horde version will come once an NA/EU guild has defeated Garrosh.
Horde world first kill by Apophasis US. In the Horde cinematic, Vol'jin doesn't want to be the Warchief -- but Thrall bends a knee to Vol'jin, as does every other Horde leader. Vol'jin then accepts the honor.
: Horde cinematic via AdriaCraft below:
Many thanks to those in our community for helping us out with the information, links, and images!