Dagoth Ur complains that large parts of ancient Chimer territory have been taken from Morrowind by Skyrim and a part of his crusade is to return the land that was taken by the Nords.

All arguments and opinions aside, what territories do Dagoth Ur consider "rightfully" Morrowind's?

It is Dagoth Ur. He probably wants a good deal of Eastern Skyrim. Though there is nothing I have seen in Skyrim that indicates Dunmer lived there 3500+ years ago. Does he comment on the lands lost in the Arnesian Wars with the Argonians? I dont remember.

The particular document in question does not actually stipulate when they were lost. Admittedly until the Empire came about there was a lot of border swapping and raiding along the mountains, but he does not specify when it was lost. Just that he's angry.

Black Marsh and Morrowind had border disputes in the south, with Skyrim and Morrowind on the west. Very likely, Dagoth Ur wants those contested lands, then the world. Maybe Solstheim is also part of it too, or something.

Considering that he fought most of his mortal life against the Nords and they probably claimed a good deal of now-Eastern Skyrim as spoils of war, it's probable he's referring to that territory. He did fight to claim the territory in the first place. You'd be pissed to see it taken away too, partly invalidating what you fought for.

Which parts? For a liberal interpretation of historical territory, Riften area definitely, probably extending to about where Whiterun is now, and extending north until Windhelm, as that has historically been the throne of Ysgramor and they would not have made as big a deal if the Chimer at one point occupied the city for some period of time.

Maybe the lost land belonged to House Dagoth. When they were crushed, so went the north. I don't remember House Dagoth having territory in Vvadenfell, just that the Sixth House grew from the Cabal.

Kogoruhn was House Dagoth's Stronghold. It was his capital.