So how does the manga tie into the game?
It's basically the year that Dante first met Vergil for the first time after the incident of Eva's death.
The manga was supposed to show us how Vergil unlocked all the seals/mechanisms in order for Temme-ni-gru to rise.
How Arkham and Vergil met (the extra cut-scene in DMC3:SE where Vergil meets Arkham in the library is actually taken from the manga. The only difference (that matters, cause there are a few more differences) is that in the game Arkham is already part devil, while in the manga Arkham was still human. Lady's mother was still alive and all at that point.
Dante's life prior to opening his own shop.
How Arkham became a devil.
How Lady's life was before that event, and how it changed her life forever after that.
And a few other stuff.
Only problem? For reasons unknown to me, the author never released the final chapter of the manga thus leaving most of the Lady/Arkham part of the story blank, while Dante & Vergil's part in the manga remained incomplete.