I don't get it, you are still applying the force in the same direction. I mean if you rotate the 'wrong' picture by 90 degrees you will see that they are both the same thing
The wrong movement detaches the glue from the center of the pad to the edge. The right one detaches it from the right side to the left side of the glue bar. Both directions are orthogonal.
If the adhesive edge was an axis, the article is saying to peel along that axis, whereas more typically folks peel perpendicular to the adhesive axis, causing the post-it to curl up and out from wherever it is placed.