It's clearly still an alliance - we saw Night Elves, Worgen, Dwarves, and Draenei in the cinematic. I don't remember seeing Gnomes, but they're tiny and could have been standing in back.
How the factions choose their War Chief/High King is an interesting topic for discussion.
The Horde apparently lets the outgoing War Chief name his successor, without needing input/approval from the others. Vol'jin named Sylvanas, even though she never would have been elected if the others were polled. After Garrosh died, they let his predecessor Thrall name Vol'jin. So unless Vol'jin comes back to have a say, I guess Sylvanas names the next one.
The Alliance was originally led from Stormwind because they were closest to the Black Gate, and first to face the Horde. After King Wrynn's death, Anduin Lothar was looked to as the military leader who could best lead them to victory. According to Wowpedia (for what that's worth), humans are "the primary race of the Alliance that makes up the majority of their forces". Maybe it's like western military coalitions in real life: the US winds up leading most of them simply because the US has the most men and equipment invested. Another possibility is that the various racial leaders - Anduin, Gelbin, Velen, Genn, Tyrande & Malfurion, Muradin, Falstad, & Moira - held a meeting and decided Anduin should lead? Which begs how they arrived at that choice: was he a compromise candidate because he was the only one they could agree on? I might have gone with Muradin, but perhaps choosing one of the Dwarves would have created dissension in Ironforge. Perhaps some of the others didn't trust Greymane to lead with a level head. Malfurion has his hands full with the Cenarion Circle and is far more worried about the dark armies than he is about the Horde - after all, he works with Tauren and Trolls every day. We could go on, but point is maybe Anduin represents the best choice for faction unity, even if he does lack experience. One other fun possibility to consider is that they voted, and the only one not to vote for themselves (a la Pirates of the Caribbean III) was Velen, who supported Anduin to help him on his path to leading the Army of the Light. While that's a fun option, I really don't think Anduin would have voted for himself (he probably would have voted for Velen), so idk. Honestly, I think it's just because humans are numerically the largest faction.