The way the Old Timers explained it to me was that, back in the '60s, most of them were running stock trannys (standard diffs) with relatively skinny tires and the belief was that you got the best traction with the right rear tire. So by running the drained front left shock, the theory was that the left would come up quicker than the right and transfer traction cross-corner to help you launch better.
Or something like that.
I ran them on my '67 at Carlsbad (RIP), but couldn't tell if they helped because I was too busy blowing every launch I tried. The Old Timers forgot to also add that you need to know how to drive.