Seeing the locations of the two setscrews, I wonder if it was used on a square shaft; you'd use the screw which hit the middle of a flat face. A wire or cable through the hole would permit remote rotation of the shaft through a limited arc; being able to shift the lever position by 45 degrees could easily make a big difference in how useful that arc would be. Even when directly hand operated, being able to reposition it would allow it to avoid obstructions.
I don't see much to gain from being able to rotate a square-bodied die by 45 degrees - that's what made me look for another possibility. And for square dies, why not clamp on two faces, or have a square pocket, maybe with a lip to help get side pressure to start the threading? But if the square goes clear through, and this is used as a lever, there's a benefit from the eight-pointed pocket, AND from having two screws.
