It appears to be for holding boards parallel to the top to be worked on - is there a means to attach the slotted wooden piece to the leg at the opposite end from the vise? Here is a discussion on Sawmill Creek that seems to apply to your question, even has a p/n for the clamp.
Sjoberg bench question [Archive] - Sawmill Creek Woodworking Community
Sjoberg bench question [Archive] - Sawmill Creek Woodworking Community