Burma

Burma was a region of the world under at least the nominal control of Kublai Khan in the 13th century. This meant it was likely in Asia, somewhat proximate to China. The Doctor once won all its commerce for one year by playing high-stakes backgammon. (DW: Marco Polo)

Burma was never identified as a country in Marco Polo, and indeed it certainly wouldn't have been considered one by the Khan. In real life, Burma had been captured by Kublai only two years prior to the date of the story, 1289.