No, it is. Imperial and Cyrodiil are both correct. It is the name whence the province and the people are derived. The city wasn't always the center of Empire, after all. Cyrodilics haven't always been "Imperials," either.
Cyrodilic history truly begins by the middle of the Alessian Reformation (see sidebar, Alessian Order), when civilization and cultivation had allowed the region to emerge as a discernible Tamrielic power. Its culture and military strength centered in the sacred Nibenay Valley, a grassland expanse with a vast lake at its heart. Several small islands rose from this lake, and the capital city sprawled across them, crisscrossed with bridges and gondola ferries. Rivers connected the city-state to both its profitable outlying territories and the friendly inland ports of Skyrim and Pellitine.
You must understand, Cyrodiil was a land of many races, many nations, many tribes, before their unification. Cyrodiil hasn't always been the land named Cyrodiil, and its people have not always been Cyrodilic. The city from which Cyrodiil grew is Cyrodiil.
Like I said....
When the series first started it was the city of Cyrodiil in the Imperial Province.
http://www.imperial-library.info/sites/default/files/gallery_files/mapbigtamriel1.1.jpg
Interesting. Though, it is no longer. So, I stand by my correction in the context of the games as they are now.
I understand that's what it used to be called. I'm not arguing that. I'm saying it is no longer called that just like how it would be incorrect in the context of today to use Czechoslovakia. That country has now split into two separate countries known as The Czech Republic, and Slovakia. :shrug: