About being offensive or a minconception (Yeah, it is)
I don’t know where you got the idea that it isn’t offensive; those people are called Turks, not Tatars. In fact, the entire description of “Tatars” is a fictional European construct created after 1300 to fill in an area on the map that was difficult to visit or chart; mapmakers simply used the name “Tartaria” to fill the space between Russia and China.
The problem is that “Tartaria” itself has been the subject of conspiracy theories regarding an exotic land of that name; assigning that demonym to a civilization would create a lot of confusion—especially for one that, unlike the Hausa or the Ethiopians, “never fully united.”
Tartaria Parody
I even once make a parody of Tartaria as a civilization. The goal was to explain why it isn’t a good idea to use umbrella terms or fictional countries, and I published it on April 1st:
UPDATE: By the way, the point of all that was to clarify the name “Tartary.” But yes, I would also like to see nomadic civilizations or ones from the Central Asian region, though I think there are better terms or factors to consider. For instance, you could use the Khanate of Bukhara, or—if you want a nomadic power from the game’s timeframe (1500–1800)—there is the Dzungar Khanate.