This post is a translation of what is detailed on the Japanese Soul Calibur site, called Soul Archive. The page for Soul Calibur VI can be found here.
The Japanese page for the game has far more details than what are available on the English language page.
They currently list the existence of four game modes. The first is ‘Soul Chronicle,’ the base story mode. And here, I will detail the info, as slim as it is.
This tale takes place at the end of the 16th century, following the fates of the heroes entwined by the evil blade Soul Edge. You can follow the experiences of each of these heroes, and their fates that are profoundly connected to that of the evil blade.
On the timeline menu, all of the character episodes are lined up alongside the main story. As you clear these episodes, new ones will unlock.
The origin story of this series is reconstructed through new episodes. As all destinies are spun together, rebuild the chronology of this dual-faceted sword!