"Civilizations" are a bit different... as they tend to have distinct borders, governments, and various other institutions. They are more discrete and easier to define. They're also easier to put start and end dates on. And all of these ancient civilizations have passed their end date. It's only because of the relatively recent concept of nationalism that we are even attempting to connect contemporary nation states back to these ancient and very distinct civilizations anyway.
Same for assuming that the people today in Greece *only* have ancestors who all lived within the borders of the present day nation state and that somehow their genetic material was not mixed with the ancestors of the residents of Macedonia or Turkey or Bulgaria etc. Ridiculous.
Yeah, Greeks have some DNA in common with Alexander I'm sure, but... so do many of the residents of Serbia, Macedonia, Romania, Bulgaria, Turkey, Egypt, Iraq, Iran and Afghanistan. And many others aside.
btw what religious link do you believe contemporary Greeks have with ancient Greeks? I did see some college kids there dancing to songs they had invented to honor Dionysus but the average Greek today worships a Palestinian carpenter who lived quite a long time after those ancient Greeks were dead and gone.
Look on my works, ye Mighty, and despair!'
Nothing beside remains. Round the decay
Of that colossal wreck, boundless and bare
The lone and level sands stretch far away."