First, all arguments about what Civs "should" be included - or not - are largely pointless because of the context in which you/we are all arguing: this is a commercial game which has to sell large numbers of the game just to break even, given the cost of producing a computer game these days. That means that the first consideration will always be What Civs Do People Want To Play and Identify With regardless of the historical, cultural, military, linguistic "importance"of the Civs in question.
Lots of gamers with lots of money are in western Europe, Japan, and the USA. The United States, Japan, and many western European 'Civs' will be represented in the game. Every time. Regardless of who they push out of the game to make room for them.
Second, my one and only legitimate contribution to the Rome/Byzantium/Greece discussion, because I took a degree in Classics with emphasis on the Hellenistic period and some courses from a Byzantine expert (as in, fellow of the archeological schools in Athens and Ankara, fluent in Greek, Latin, Aramaic, Turkish and Arabic), and he made an important point that is applicable here.
After introducing his graduate level class to the basics of the Byzantine world, he gave us a lecture on "The Trinitological and Christological Conroversies in the Byzantine Church in the 4th - 8th centuries AD" - and by the end of the hour not one person hearing it could have told you anything intelligent about what he had said. It was absolutely Unfathomable to all of us from start to finish.
At which time he told us that the point of the lecture was, in fact, that it was unintelligible to us. But these controversies were so important to the people of Byzantium that they would riot in the streets over them.
Lesson: People in the past are Not Like Us. They may be living in an urban, cosmopolitan, international city like Constantinopolis/Byzantium, but they do not think the way we do, or even about the same things.
So the larger lesson is that it is immaterial whether we think the Qing, Jurchen, Manchu, Yuen, etc. are "Chinese Dynasties", or how the Greeks, Byzantines, Late Imperial Romans considered themselves or were similar, identical, or utterly different. What really matters in both understanding them and representing them in-game is What that meant to them at the time - and you can bet solid money that how they thought about it and themselves and their neighbors was not how we would or do think about those things.
Oh, and as to the Greek language vis-a-vis Byzantium: Istanbul/Constantinople was a majority-Greek speaking city until the beginning of the 20th century and had been the largest Greek-speaking city in the world for about 1500 years at that time, while ostensibly being "Roman", "Byzantine" or "Ottoman". The language had little or nothing to do with the politics of the times, and was only one component of the culture of the city or the polity of which it was part.