This asks the question, what could happen in between Skyrim and TES6 that would make the outcome civil war, along with most of the events in Skyrim not important, and no, hundreds of years passing by or it just not being mentioned isn't good enough. We need some kind of anwser, maybe in the form of a book or just hearing about it in TES6.
Here is my neutral proposal. The Empire begins to crumble. In Skyrim, the civil war has deteriorated into a full blown war between the holds and Jarls of Skyrim, with the Stormcloak Rebellion or the Imperial Loyalists not being able to control Skyrim. With Reachemn besieging Markarth in the west and Falmer launching attacks on the surface world in the east, and Ulfric Stormcloak dead, killed at the hands of the loyalists, Skyrim seems doomed. Then, as the Emprie crumbles, the Breton kingdoms of Farrun and Jehanna unite into the Kingdom of Wrothgar and make an alliance with Solitude, Morthal and Whiterun. The Nord King of Wrothgar marries Elisif and liberates Markarth, taking the Reach as his hold. This covenant takes back Whiterun, Dawnstar and Falkreath. Winterhold surenders and Windhelm and Riften follow. The Nord King is made High King and this hero now poses a threat to the Thalmor. It is said they were the chosen of Kyne and actually met and fought alongside the Dragonborn after the events of Skyrim.
They also were a raider, known as the scourge of the Sea of Ghosts, taking over several islands between Atmora and Tamriel, including Rosecrea. This hero would want to create the Second Empire of the Nords and would pose a bigger threat to the Thalmor than the Empire did. A post Season Unending Skyrim, a hero with the ideals of the Stormcloaks, but the views of the Imperials. A true Nord and chosen of the gods.