Turks: No cities here, all they did was conquer from others anyway.
Dude, you used to be the most reasonable Armenian I knew, and quite knowledgeable. I understand your urge for Turk-bashing, but at least do it sensibly (i.e. with some research). Just as you would get annoyed when some uneducated Turkish nationalists claim Armenians never had independent kingdoms, your statement is annoyingly and blindly offensive.
From the top of my head, Urimchi (Urumqi), Kasghar, Yarkent, Beshbalik (Besbaliq), Semerkand, Kargalik, Tashkurgan, Tashkent, and possibly Buhara (Bukhara) and Merv (but these last two might count as Persian as well, Turks and Persians did not have a clear-cut cultural border on the central asia side) were some of the historical cities. If you need more, I advise you grab city names of today from Turkestan, as most of these were historical cities on the silk road. (Turkestan is the region including Kazakhstan, Uzbekistan, Kirghizistan, Turkmenistan, and Sinkiang-Uigur province of China).
Of course from a different point of view, with your map and start date, you shouldn't even have Turks in the game (not simultaneously with Tatars at least). For more than half of your timeline, the only Turkic peoples in your map is Tatars, northeast corner of your map.
