First of all, motion should not be steady and preferably not always in the same direction. The goal here is to make your own fists harder to hit. Since you have no gloves to protect you, they are a valuable target.

As for the position of the hands, pugilists used it to keep distance from opponents. That's also a reason why they sometimes leaned a little to the back. Boxing 'guard' does not work in pugilism for two reasons. One, you still have no thick padding on your hands to work as a protection. Two, in pugilism grappling and kicks were used as well. Also punches are thrown differently in bear knuckle fighting. This "old-timey" stance take this into account as well. Check here.