In a era when decimal numbers didn't exist, but fractions did, 60 has many factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60. The factors of 10 are: 1, 2, 5 and 10.
When dividing quantities into smaller units it is easier and more useful to be able to divide them into the smaller quantities if a base of 60 is used instead of 10.
I found something, but I don't know how it jibes with the context you saw it in.
I came across a presentation by Chaogui Zhang titled History of Mathematics: Hellenic Traditions that actually defines the period as 800BC to 800 CE. If I'm reading their slides right, they seem to be implying a shift of historical focus from river valley civilizations (Egypt ...