The first travel from Europe to Karakorum happened much earlier (1216), so that European cainites have the opportunity to have heard of Karakorum and travel there, without needing to wait for William of Rubruck's travel in 1254.
Construction work in Karakorum already begins in 1220, utilizing workers from Chinquai Town and the Khwarazmian campaign.
The Battle of Indus in 1221 ended up as a greater success, and the two tümen (20,000 Mongol soldiers) stationed there under the command of Dorbei and Bala managed to establish a small but steady presence at the northern edge of the Sultanate of Delhi. This provides an easy springboard for Indian cainites early on.
Martial Arts: The historicity of many of the martial arts is dubious (often attributed to legendary sifus or monks of ancient times), and by the 13th century they almost certainly didn't exist in the formalized form known today. Regardless, it is assumed that they already exist and somewhat resemble the form known nowadays, to make use of the material found in SF:STG and to make it easier for players to imagine and research what they look like.
Some like Yagli Güres are definitively relatively recent inventions - but I'm fudging their origin, to give the cultures more variety in choosing styles.
Majestic Crow Kung Fu is completely fictional and directly lifted from The Perfect Warrior for SF:STG, as it is a balanced style that fits well in with the other Chinese styles.
Baraqa is a fictional Middle Eastern style found in Contenders for SF:STG.
Dirty Fighting and Kherüülch ("thug" in Mongolian) don't represent actual fighting styles, but a no-nonsense no-holds-barred approach to hand-to-hand combat well represented by the existing Special Forces style.
There are no Kuei Jin. There are rumors from the edges of the Mongol Empire, but kuei-jin will never show up and feature in the game.
