The games do not necessarily have to be completely accurate, but should allow for a dialogue in the class to discuss inaccuracies and compare to our coursework. I'm not entirely sure AskHistorians is the best subreddit for this, but I assume I would receive much better answers here than a gaming subreddit.
How ancient would you like the game to represent? Rome II: Total War has a fairly realistic look at logistics and armies of the time period, and an interesting look at some of the (very high level) politics. Shogun II: Total War as well for the samurai-era in Japan.
Have you considered board games as a complement to the video games, or is it directly about video game concepts?
I had a teacher in Middle School that actually did in-class simulations dealing with the ancient Near East and also Rome. His name was Brad Hulman, and I know his simulation was published. I'll try to find it.
And my favorite simulation:http://www.interact-simulations.com/c/product.web?nocache@13+s@aSosq6kZqQf6k+record@TF34287+Title@EMPIRES+ISBN@9781573363754
I'll never forget doing these in class. I used to spend my gym period every day strategizing and planning what to do next in the simulation. Empires was amazing.
Ancient world history is super broad. If you mean Antiquity your best bet is the Rome: Total War games and perhaps EU:Rome.
If you mean up to early middle ages I can suggest games like Crusader Kings 2.
I don't know much about anywhere other than the ancient Mediterranean world, but it is heavily under used field imo. Good luck with that
In addition to the Total War series that others have mentioned, have you had a look at any of the old school city builders like Caesar III, Zeus+Poseidon, Pharoah+Cleopatra?
There is a combat element to some of the missions but they're way more focused on trade and city development.