It's another one ported from PS2.
I haven't finished watching the anime and I haven't started playing this game, so I don't know if the anime covers this one or not. (But for the first few anime chapters that I've watched, they followed the plot in the first Hakuouki quite closely.)
And I know a few girls who would scream with joy if Hakuouki series were yaoi.
By the way, it's not fun to play if you can't read Japanese, but the graphics and voice actors are worth it. You can just leave it on auto and listen to the voices when you're doing something else. (If it's like the first game, you just click the choices every once in a while. Anyway, it's very likely that you will get bad endings if you keep choosing the wrong answers.
)
Edited: Tried the game. I don't think you'll get bad endings for this one. But you need to choose the correct choices to progress to the later stories. This is much easier to play than the first game. It's like a collection of extra stories from the first game and you don't have to go through all the tragic parts.
Google search with the game's name can give you some websites with story synopses and some scenes' translations too.