It is true that Sylvanas was never human. But the fact that Arthas murdered his father and turned all citizens he could reach into mindless undead changed the political map of Lordaeron forever. Before, Lordaeron is a human kingdom ruled by Menethil family. But after Arthas left and Lich King's control over undead weakened, the Lordaeron is reverted back to a lawless land where no one or no organization would put a solid political claim. And its population was also changed from mainly human to a mixture of undead humans, undead elves, etc.
In this political vacuum, Sylvanas rallied the freewill undeads, killed dreadlords and their minions, as well as some remaining living humans. She then proclaimed a founding of a new kingdom of undead over the ruin of Lordaeron, and she was able to hold it and even expand it afterward. Her kingdom was also recognized by the horde, the second largest pan-Azeroth political organization, as well as Argent Crusade, probably the strongest neutral faction on Azeroth.
In all theoretical and practical senses, she had unrepeatable legal authority over the kingdom she built from scratch. And she did have the support of her subjects. If forsaken is going to hold a democratic election, she will still be their leader.