Since Skyrim had two possible endings to the civil war, the next game will find a way to make them not matter. Ulfric Stormcloak can die, so he will die. General Tullius can die, so he will die. Elisif the Fair can't die, but was originally meant to and would be repaced with Erikur. So, this points that originally, there was supposed to be an ending that would render the civil war ending pointless. But since Elisif is still alive, she will most likely take the throne, Stormcloak or Imperial victory.
Here's how I would handle it. The war rages on for years and the Dragonborn is said to have played a part in the war, but on which side he fought was lost. Ulfric Stormcloak will be killed in battle, most likely by the Dragonborn, or be challenged in ther old way by said hero. He might also be assassinated by the Thalmor. Tullius as well, could be targeted by the Thalmor or the remainign rebels that were still loyal to Ulfric. Let's take Torygg as an example. He had two choices. To live in dishonor or to die with honor. He chose death.
Elisif the Fair, Torygg's widow, is the only player in the civil war, besides the Last Dragonborn, that doesn't get killed in either path. She was meant to be klilled during a scrapped Daedric quest. There are a few ways to render the end of the civil war mute.
1. Great Cataclysm
Some great cataclyms destroys Skyrim like the Red Year or the Great War and renders the ending moot. This could have something to do with the Thalmor, the Dragons or something new.
2. Season Unending
The war continues on and no one is sure who is winning because of the chaos. The war is still going on or has just ended and Skyrim was ravaged by this bloody war that Ulfric caued.
3 Imperial Resolution
At some point during the war, Tullius and Ulfric are both dead, and the Emperor's death causes a power vacuum in Cyrodiil. Fighting breaks out throught the province and factions begin fighting for power. One of these factions rallies the nords, both rebels and loyalists, by promising to lift the ban on Talos worship. The nords conquer northern Cyrodiil and capture the Imperial City. Blackwood is lost dough, to both Argonians and the Dominion. So, instead of the crumbling Mede Empire, you would have an up a coming Nord Empire. This would be about twenty years after Skyrim.
Since so much was cut from the civil war, I think the third option is the best. Otherwise, if the things that were cut stayed, it would have to be between number 1 and number 2. And this is not a Stormcloak or Imperial thread, or a Civil War thread, but a third option that would satisfy people for the next game. And no, the High Hrothgar Peace Treaty should not be the canon ending.
Also, what do you think the Dragonborn's excuse should be for not being in VI? Nerevarine was rumored to got to Akavir. Hero of Kvarch became Sheogorath. My guess is that the Dragonborn could go missing during that war in Cyrodiil, and could be presumed dead, while some believe they are still alive. There needs to be a set ending for the events of the game, the outcome of the war needs to be vague. If they kept it like it was meant to be, we wouldn't have this problem, as there would be chaos.
I personally think that since Elisif lives in any scenario, she will eventually become the ruler of Skyrim. She will grow into her role as High Queen, the war and her advisors shaping her from the caring and mourning widow to a strong queen and even a warrior queen of sorts. A warrior like Ulfric has no place on the throne, but on the battlefield. And yes, I am a loyalist, but because I hate Ulfric, not the Nords.