The original victory condition is to regain all the Korean city at some time after 1600 but within 100 turns. But instead can one win by capturing Kyoto and Fe Ala, under a not-too-easy level?
the answer is yes and no.
Yes, in this case you will win the scenario (because if you play either Korea or China and survive until the end of the game AND have the highest score, you'll win).
It's incredibly hard though, to conquer the Manchu. Mainly because if you play China, Korea will make peace with them whenever possible and vice versa.
Capturing Japanese cities is possible, but it takes a while to get to Kyoto. On Deity I managed to capture 3 of their cities. More wasn't possible in time.
Read more about it in my Fear the Turtle Steam Achievement Guide