I haven't seen neither the first anime, nor played any of the games either, so I had a hard time figuring it out too.
But I think you are right, and that's also what I wanted to say before getting fed up to make heads and tails out of all the stuff.
According to VNDB and AniDB: the first game,
Koihime † Musou ~Doki ★ Otome Darake no Sangokushi Engi~ is the one with the already finished mediocre anime (no english translation for the game).
However Mangagamer licensed it's sequel,
Shin Koihime † Musou ~Otome Ryouran ☆ Sangokushi Engi~ , and that's also the one title which might receive
an adaptation in autumn. Which means we might play and watch the anime at the same time, and that'd be quite good if it happens.
So yeah, if I'm correct Mangagamer licensed the second title of the "series", probably a continuation of the anime we might know here on the west.
Is there anyone here who played the game in japanese or korean anyway? It would be nice if someone could confirm they are indeed the continuation of the existing anime, how necessary is it to know the "first title", and I'd be interested to know how good of a game is it. I'm really not the most reliable source to summarize the relations between stuff I'm not entirely confident.