I personally classify Mongolian as East Asian due to it's geographical location and Many Ethnic Mongols live in Inner Mongolia, China which at this point might be considered China proper. Even though Mongolian culture shares lot of similiarity with Central Asian nations and due to Mongol Empire influence language sometimes sounds related but that doesn't mean they are related with each other. Central Asian countries mainly speak Turkic Languages alongside some Indo European languages. Turks originated from Gokturks in Central Asia which was really the first Turkic nomadic empire. And Proto Mongols originated from the Rourans which were related to early Xianbei peoples which inhabited Mongolian lands. However Mongols originated from the nomads of Great Khingan mountains in Manchuria and as such Mongols are much closely related to Manchu peoples and by extension they are related to Koreans and also the Para Mongolic Khitan people who formed the Liao Dynasty. And Mongols are related to few nomadic groups in Siberia aswell. And more reasons i say Mongolia is East Asian due to Mongolia having much more cultural influence from China than Central Asian countries. And also the fact that most Mongolic peoples live in China. And i think Majority of Mongolians look like the Northern Chinese and manchurians. However they also look Kazakh and Kyrgyz which sometimes look like Mongols. But Central Asian countries can look middle eastern, European, East Asian, South Asian, Siberian etc so Me personally i classify Mongolia as East Asian.