Throughout history, population size has evidently not been a good indicator of degree of influence upon the long term development of humanity over all. In the last 400 years the influence of an average of at most a couple hundred million people of European descent upon the world's development in general has most certainly vastly surpass the combined influence of many more hundred of millions of people of Chinese or Indian descent. If you look back throughout recorded history, I think you would be hardpressed to find many eras when size of population had been the best predictor of which cultures would excert the greatest influence upon course of overall human civilizational development over the succeeding centuries. Expansion, aggression, cosmopolitan mindset, eagerness to promptly absorb and adapt useful foreign influences much more accurately predict which cultures would be influential, and which ones despite its mass won't.
Regarding the arbitrary classification of cultures into your 6 catagories, If you are to take your notional array of six cultures and analyze the web of mutural influences that have effected their development through the ages, you would find several of these clearly shared much more closely interwoven web of mutural influences amongst themselves than they do with others. You might say Greek and Roman heritage for much of the root from which the main trunk of 3 of your 6 cultures, American, European, and Slavic, sprouted. The heritage of Alexander also had more influence upon Islamic culture, both through direct influence of Hellenistic culture down through the ages to the Islamic lands they occupied, and through the influence of and transmission from Greco Roman world through Byzentium and through Cordoban Spain, than you might have imagined in your sterotyped vision of different cultures. So you might say the world of Alexander form major part of the root of 3 of your 6 cultures, and significant part of a 4th. Your Qin formed significant part of the root of but one.
At this point I have to step back and make an observation about your classification of "civilizations". I have to observe that it seems to be something of habit and characteristic of the Chinese culture to seek legitamcy in its own perceived heritage, and seek wisdom in the past. This predisposes the Chinese to regard themselves as primarily the continuation of some past they revere, and play down the influences they had been compelled to absorb down the ages from what they consider to be side tributaries.
This mode of self perception was also briefly in vogue in the west from mid 18th to mid 19th centuries, when educated classes of western Europe would consider it as evident that modern western civilization is the direct continuation of Greco Roman heritage, and it is suitable to seek legitamy in Greco Roman philosophy, and seeking wisdom from Greco Roman practice.
But the main current of western self perception has moved on from that mode. It is now recognized that cultures are an amalgamation of highly useful influences from large array of different sources, some keenly perceived and woven into a culture's preferred narrative of itself, others unconscious but nonetheless just as influential upon the modern menifestation of culture.
Perception of culture has moved on from an attempt at nationalistic self-justification, to a somewhat more objective assessment of the interwoven web of mutural influences.
