Pretty much all of pre-colonial Africa, save for Egypt, is fairly unexplored. North and South America pre-European contact are similarly unexplored, except maybe the Aztecs, Maya and Inca, although pre-Colombian South American civilizations tend to be used as "Civilizations" rather than as settings. Pre-colonial Austrailia also could use a bit more coverage, as could Australian history in general really, in fact most of the Pacific is pretty unexplored, yet there are so many interesting peoples and cultures that in habit that area. Likewise almost all of Central Asian history remains pretty underrepresented in video games.
Actually, decolonization would be interesting as well. Playing as an oppressed African or Asian freedom fighter as he struggles against his oppressive European colonial overlord. There are so many games about colonization, it would be great to play one from the other side, one where I don't feel like the villian.
And like the original poster said, it'd be nice to see an exploration of classical civilizations that aren't Rome or Greece, so places like Iran or Carthage would be cool. I would also enjoy seeing more of post-classical Rome, the Middle Ages is a pretty well covered era, but the Eastern Roman Empire only rarely gets any exploration or even recognition.
Islamic history also tends to be ignored in most video games. From the early Middle Ages all the way up to today, Islamic History is filled with fascinating people, stories and places and the Islamic world has extended throughout Spain, across Northern Africa, into Eastern Europe and the Middle East and all the way into China. It would be fascinating to see a game to take place in the Islamic world, or even a fantasy Islamic world as opposed to Christian Europe or fantasy Christian Europe
The Indian sub-continent could also be really interesting to explore. India really isn't a homogeneous whole, like it is often portrayed as, it's more like Europe as a whole than any one particular European nation. There are so many different cultures, peoples and languages in the Indian subcontinent and for most of it's history it's been dived into hundreds of kingdoms and monarchies competing for supremacy, not unlike Europe itself. It would be fascinating to see a game that took place in India, maybe a Crusader Kings style game where you build up an Indian kingdom, or maybe something like Assassin's Creed that takes place in an Indian Kingdom where you can explore different places really see the continent close up.
History is so vast and so interesting, filled with amazing stories and fascinating people. It would be impossible to cover it all, but at the same time it would be nice it video games would explore some more parts of it then they tend to, it get's kinda sad seeing the same settings visited again and again.