Around when is this supposed to take place? I see Troy is still there, Athens is not, maybe these are clues.
I know that computer games are not exactly the best place to look for historic accuracy, though when there is some, I enjoy the game even more. E.g. I enjoyed the infotainment aspects of the Castles series

Imo it depends on campaign. Most of them are based in mythological period (might be 1200-1000 b.c.) - conquest of troy, ancient sparta, greek heroes etc. Only few missions are based in colonization era (around 900-700 b.c.). Sadly no "classic greece" (after 500 b.c.) scenarios as far as I remember.
Considering all the gods & heroes appearing here it's definitely mostly mythological-based game. Does it really matter? You're not going to learn greece history here :P Even this mythology isn't completely accurate. It's just a game :) Pretty damn good game I mean.

Thank you. I saw now that it said in game what the year is, something around 1300 b.c., I believe.
Of course this is no history simulation, but when they make a game in ancient greece, it is nice to have as many historical references as possible. I am still in the tutorials, though.

Don't buy this if you want to have the feeling of taking part of the development of an ancient city, buy Caesar III or Pharaoh instead.

This one feels more like managing a Las Vegas Theme Park or running a city from a Saturday morning cartoon.

Campaigns happen in different times, and there is history alongside myth. I remember Peloponnesian and Greco-Persian wars (I think they were in Athens campaign, but I might be wrong).

The game starts in the Golden Age of Greece--- the Mycenaean Age. Homeric tales were of this Age. It was a bronze age culture that was considered Heroic (think 1400- 1100 BC). The game then moves into early Iron Age Greece with the advent of Sparta, Corinth and Athens. The game then goes to the Athens-Sparta struggle which is nearly the end of the Greek Civ (300 BC).

(Thebes destruction by Alexander the Great in 335 BC. Thebes was the last City State to oppose Macedonia "leadership." They revolted when Alexander took the throne on his father's death. Athens sat it out. Wasn't destroyed but wasn't really Athens ever again. That would be the end of Iron Age Greece. What follows under Macedonia would be called Koine Greece.)