This is interesting, because most depictions of the Illiad and the Odessey are 1) blown very much out of proportion to what would've been accurate. 2) A lot of the ancient Greek epics were based on previous stories from the Caucasus, being reset to ancient Mycenae. Similarly, if you look at the wikipedia page of 'Heart Of…
The closest thing to memory fitting your desired setting is a 3D adventure/action game from the 1990s titled Quest For Glory III: Wages of War. It was developed by Sierra back when the company's prime focus was on quest based puzzle games. Some here will recognize such titles as King's Quest, Space Quest, Police Quest,…