Syntax, you are correct. The right and left verison differs because of which side the bevel is on when the blade is in a cutting position. The picture in the video and on the website opening page is a right hand verison. This means that the "bevel" is on the down side IF you are holding the knife with the spine against your hand. The south paw verison is just the opposite. Quick trivia if you didn't know it.
From what I remember reading, most ball parks were orientated east and west. Therefore a left handed pitcher had his pitching arm on the South side of the field, henceforth "Southpaw".