The Byzantine Empire's government and administration is basically not represented at all. They are essentially a clone of the Western European countries - an understandable design decision, as Paradox didn't want to have to create an entirely new governing system, but not a historically accurate one.
As it has been said, Byzantium in the eleventh century was an empire governed from a large, sophisticated bureaucracy based in Constantinople. The bureaucracy was as close as the Middle Ages ever came to modern 'professionalism' and required a formal education in literature and rhetoric. Although the official language was Classical Greek, it was a multi-ethnic administration; historical sources contain many references to Italians, Slavs, Bulgars, Armenians, Georgians, Turks and Cumans (among others) in the government.
The empire was divided up into various provincial units (Themata, Katepanikia, Kleisourai, Archontiai etc.) that were not uniformly imposed across imperial territory but rather based on local conditions. These were governed by a military aristocracy which was in theory subservient to the civil administration and the emperor in Constantinople. Military leadership roles were not hereditary as in Western Europe, but were rather appointments made by the central government. They were often rotated, with various commanders being given authority over several different administrative units over their career. Although Byzantine aristocrats did own hereditary land, and although Byzantine provincial administration gradually became somewhat more similar to the western 'feudal' model over the centuries through the introduction of e.g. the pronoia system, Byzantine society was not ordered along western 'feudal' lines.
Ultimately CK2 does an exceedingly poor job of representing Byzantine government and society; or, rather, it makes no effort to do so. However, the designers presumably felt that the effort in research and implementation was greater than they could justify.
