Middle Chinese (jìndài Hànyǔ 近代漢語, also called zhōnggǔ Hànyǔ 中古漢語), refers to the form of Chinese spoken from the 3rd to the 13th century AD. It is further divided into Early Middle Chinese (for your Táng games), and Late Middle Chinese (for your Sòng games).
As written on p20 of the rule book, Middle Chinese can still be considered as a unique language throughout the Empire. But one's accent will always give their origin away as a Northerner or a Southerner.
Middle Chinese is probably when the Chinese languages got their tones, as the result of a reduction in the number of consonants and vowels. It is probably also when many compound words have appeared, to reduce homophony issues.