They fought with the Byzantines and the rising Muslim Caliphates as well, two civilizations that belong in the second age. In Civilization VI we had Greece and Macedon, not Greece, Sparta and Macedon. The southern Greek city-states and the northern Greek kingdom of Macedon coexisted during the same time period. On the other hand, the Achaemenid Empire and the Sassanid Empire never existed at the same time frame. This is like suggesting that Rome and Venice should exist in the Antiquity Age, which would be erroneous.
I'm not suggesting that the Timurid Empire and the Mongolian Empire should exactly have the same traits, but both of them were Mongolic. Again, this feels like having Scotland and Ireland in the same era, both of Celtic heritage. Should we get the Timurids in the Exploration Age? Maybe we should, but not as a replacement for the Sassanids, the true successors of the Achaemenids.