The sun-centered system pictured in the lower window of the video offers a simple explanation for observations of apparent retrograde motion. should these facts alone have been enough to convince the ancient greeks that earth really does go around the sun?

No, because the Greeks had an Earth-centered model that also accounted for apparent retrograde motion.

Explanation:

The Sun-centered picture that is present in the lower window of the video offers explanation about the retrograde motion is not enough to convince the Greeks because they had  an Earth-centered model that also had the same motion.