The Alliance follows the humans, more or less, and the humans in Azeroth rule by blood right. In the Horde, they follow the Warchief, and the Warchief rules by might. Vol'jin's revolution found the allies needed to dethrone Garrosh. What we basically saw in that cinematic was a symbolic display of submission, not only by Thrall but by all other likely challengers for that rule by might, they all take their turn to "bare their throats" to him, if you will. Popular sovereignty really isn't a factor among the races of Azeroth.