Blizzard has been working in a lot of different media to promote their expansions, and with Harbingers they continue the animation style that they began with the Trials of Shaohao and later with the Lords of War shorts.
The first episode of Harbingers arguably could have been a Lords of War episode, but it's told from Gul'dan's perspective. We don't really learn a great deal about the specifics of his backstory - in fact, Gul'dan explicitly says that no one alive except for him remembers the name of the village in which he was born, and then he goes on to tell us why.
I suppose this is all spoilery, especially when I get to the Anduin comic, so let's do a cut here.
Gul'dan's story does give us some information about his younger life, though it's the kind of thin you could probably have guessed. It does do away with the idea of him being the apprentice of Ner'zhul, and even suggests that he might not be a member of the Shadowmoon Clan, which in the original story was his backstory.
Granted, the Gul'dan we're dealing with in Legion is the one that we faced in Warlords of Draenor - not ours. The one from our universe died during the Second War (though given that this one has gone to the place where his Universe A doppelganger died to open a portal for the Legion, it wouldn't shock me if he found some way to pick up the memories of his other self.) But anyway, given that there are clearly some significant differences between the universes (like Garrosh being born or not being born, or Rulkan being alive,) it's perfectly believable that "our" Gul'dan did indeed study under Ner'zhul and then decide to take a different route with his magic, while this one went a different way.
In the first Harbingers story, Gul'dan is a young orc - probably only a teenager - and he is being beaten by his village's chieftain because he is weak and crippled. He requires crutches to get around, and Orcs have a real fear of weak things. While the town's shaman tries to reach out to him, suggesting that he seek out his destiny at the Throne of the Elements, Gul'dan is ultimately ejected from his village.
Gul'dan wanders the wastes (I'd guess northern Gorgrond, given the vultures and desert look to it) and nearly succumbs, but finds the resolve to seek out what the destiny the shaman had told him to find.
He drags himself to the Throne, even more broken and emaciated than before, and to his amazement, the elements swirl around him, spirits reaching out to him in a kind of harmonious dance. He reaches out to them...
And they retract. The elements reject him. Did they sense his dark future, and in so doing seal that fate? Or perhaps the elements realized that within Gul'dan was an imbalance - he had been treated poorly, to be sure, but his desire was not to find a place within his world where he could live peacefully. The elements reject him, and Gul'dan's one shot at redemption within his Orcish world evades him.
But there is another force at work, despairing of his rejection, a new voice calls out to him. It is a demon - presumably Kil'jaeden. The demon offers Gul'dan a gift - the strength he will need to serve them.
Gul'dan returns to his village some time later. The chieftain is enraged that he has returned from his banishment. But Gul'dan is no longer afraid. Instead, he burns his people, draining the life out of them one by one. Finally, he comes to the kindly old shaman, thanking him for sending him to meet his destiny before he burns him as well. The village is destroyed, and Gul'dan gladly accepts his role as the Harbinger of the Legion.
What of Anduin, then?
The Anduin comic does spoil one major event from the pre-expansion patch that has not gone live yet.
Last minute spoiler warning.
Anduin, some time in the future, sits reading a journal entry he wrote in the present day. He reflects on the letter he has received - the one that Varian is writing in the Legion cinematic. It is the last letter he will ever receive from his father. Anduin is now king.
As he contemplates his role and responsibilities in the war against the Legion, he is attacked by a Dreadlord who had disguised himself as one of his guard. Anduin uses his power to bind the demon before he can strike. The demon mocks him for being a soft-hearted idealist, a disappointment to his warrior father and a leader who will only witness the collapse of the Alliance. The Dreadlord suggests that the only path that will save his people is to convince them to join the Burning Legion.
But Anduin is not so soft. He wants peace, to be certain, but he also recognizes that sometimes to achieve peace, one has to fight. He burns the Dreadlord with holy magic and prepares to lead the Alliance against the Legion.
And then, many, many years later, an elderly Anduin Wrynn sits within the Exodar, preparing for the "final fight." Flanked by his mentor, the Prophet Velen, High King Anduin prepares to lead his people in the ultimate war of the Light against the Shadow.
There's a lot to unpack here, of course.
First off, assuming this isn't some "alternate future," Anduin's going to survive Legion and probably all of World of Warcraft. That doesn't shock me too much. But consider something: we know from Chronicle that the Burning Legion is not really the ultimate manifestation of Shadow. Demons are really beings of chaos, and chaos is the essence of Fel magic. In fact, while the demons did not seem to have any problem with the Shadow before the Legion was formed (Sargeras started down his path when he found a group of Nathrezim working alongside another planet's Old Gods to corrupt its Titanic world soul.)
The opposite of the Light is the Void, which is where Shadow Magic comes from and also where the Void Lords, who created the Old Gods, live.
I get a strong impression that the story's endgame (an endgame we will likely never see in-game, as I doubt even WoW could last another fifty years to make Anduin look that old) will see the Burning Legion long since defeated (perhaps even within this very upcoming expansion) but the Void Lords arise as the true big bads of the Warcraft Universe.
Ultimately, these reveals might not mean much for the lore of Warcraft - it's all stuff that's happening a long time from now. It does mean that Anduin and Velen look pretty safe from getting George R. R. Martin'd (Velen B died, so we already experienced that,) but we have no idea what the fate of the Horde or the other Alliance races are - other than Anduin, you only see Draenei on the Exodar (and I'm just assuming it's the Exodar.)
Anyway, Blizzard is definitely pushing a lot of these free online bits of media (there's going to be an audio drama as well,) which does at least mean you don't have to buy a book to find out about the new lore, though of course I think it's best when that stuff happens in game (there are quests coming soon as part of the pre-expansion event that talk about the fact that Azeroth is a Titan and such, which is good.)