I don't think Qing should necessarily conquer Ming, rather that Ming should fall most of the time, and whover it falls to (such as Zhou) should properly conquer it, rather than Ming existing as just a fraction of what it is. Perhaps Machu should conquer Ming a little more often, though, but the truth is, that even if we have the Faction mechanic to weaken Ming, and help its decline, we still don't have anything to help whoever conquers it to really form a ruling dynasty. Ming just gets smaller gradually, and this really doesn't seem to be anything historically plausible.
I don't really think they should get the Qing tag, though, however. Especially when some nations such as Zhou already have a dynastic tag already. The aspects China's centralisation and decentralisation aren't properly modelled properly in the game, I suppose. If Manchu manages to conquer Ming, its encouragement to properly annex it and move its capital is handled with missions. This means that we don't see potential conquerors acting as they would realistically, except for in the case of Machu, which has all these missions and events made for them to encourage the historical outcome.