The idea was, that spike failed to deliver the crystal heart to Princess C. (or Shining Armor's aim was a bit off) and King Sambra was the winner. Twilight is corrupted by him and the dark magic she was using willy nilly and is now Sambra's evil right hand pony. It was just an idea.
It does strongly hint that the world could turn dark and evil of Sombra got hold. Celestia states that the empire is practically the heart of the world. The state of the Crystal Empire will be reflected on the rest of Equestria.
In summary peaceful empire= predominantly good (pretty much) Evil hate filled empire= dark nightmarish Equestria.
I think that in taking over that plot of land out in the artic would be effectively the same as ruling the world.
But how would they get back to Canterlot? Twilight was trapped in a circle with an anti-teleportation ward on it, Shining Armor was completely unable to use his magic, and Princess Cadance's arcane abilities were limited to levitation due to exhaustion.
RD and Fluttershy may have been able to fly them them out, but they would still be sans Twilight.
First off, he'd smash the crystal heart into pieces.
He'd try take control of the empire with his powers. Twilight still imprisoned in the tower, the rest of the mane 6 would feel powerless, but they'd try to fight back. With Cadence with now magic power left and Shining unable to cast a spell..... yeah, they'd be in in trouble. Unless they find a way to contact Celestia about the situation. Now, I'm sure Luna or both of them would go, bringing the elements of harmony with them.
Twilight being corrupted? I think he'd rather turn her into a slave. We don't know if he can corrupt someone.
Beautiful work. But I prefer good, adorkable Twilight.
Since Sombra was the one who hid the Crystal Heart in the first place (who do you think created the Door of Fear, that secret passage only accessible via Dark magic, the Endless Stairs, or the anti-teleportation trap? Not the Crystal Ponies...), I think the implication was that the real Heart couldn't be destroyed so easily, forcing him to instead hide it away so that nopony would ever see it again, like the old librarian said.
I think he might have some trouble corrupting Twi THIS thoroughly, but it's easy to believe that he could exploit her little dabbles into his style magic. If he'd gotten the heart, I think his first target would have been Cadence. She's the one that caused him the most trouble, and she'd have been an easy target. The mane 6 wouldn't have the elements, which takes out their insta-win condition. He'd leave Twi locked in the tower, probably target Spike next, then pick off the others one by one. By the end, Twi might just be broken enough to be fully corrupted.