You are right Aymar,

The Avars in the game are not original Avars. I think they are the Kabars, which are the decendants of the original Avars. Avars were pushed west by the Turkic/Mongol tribes in the Central Asia and they settled in East Europe where they founded Avar Khanate in 502 AD. They fought Bulgars and Slavs as an ally of the Byzantine Empire and controlled the territory between Volga and Elbe rivers to Baltic Sea. They were defeated by Charlemagne in early 9th century. After this defeat three Avar tribes, known as Kabars in sources, settled in Transylvania. Later Skelezy tribes represented the Avars in the E.Europe.

Actually real Avars were settled in Caucasus and we see their mention in the sources once again in the 19th century, where Imam Shamil rallied Caucasus against the Russians.

So, surely there were other powers dominating east Europe than Avars in the 11th century. But, perhaps CA had other sources and think that Avars formed a social-military elite in the east Europe.