There is an Allempires article about the Khwarezm empire
Basically, the empire was founded by Turkic rulers appointed by the Seljuks.
The demographics would have been predominantly Turkic and Iranic with some Arab quaters in large cities.
Kunya Urgench one of the major cities of the Khwarzemshahs and Seljuks, which was home to many distinct architectural works including tombs of the Kagans, shrines and huge minarets was razed to the ground.
Only recently the lost city of Jend was found in Kazakistan, Jend was one of the first cities which newly converted Turks founded and was the power centre of the newly formed Seljuks. Tombs and buildings dating to the 9th centuries are being excavated. This city was totally destroyed by the Mongols, literally wiped off the map for centuries.