Yes, the Golden Horde should be a medieval scenario.
However, from what I read here, it doesn't sound like you are playing as Mongols in this scenario. It sounds pretty similar to the Poland scenario (that has the Golden Horde in it btw, but a completely different scoring mechanism). Maybe this was a first and later unused attempt at Jadwiga's Legacy scenario? Another scenario where you are a middle or east European civ and defend against incoming barbs from the east seems way too similar, even when the scoring is different. As Golden Horde, they could of course be the enemy of a medieval Persian empire, but then the classical reference would again not fit.