No stretch should cause ANY discomfort, and ESPECIALLY not pain in your knees regardless of the most limited flexibility. There is something wrong with the body positioning, kinetics, and or form of the stretch in question. You should really never even FEEL a stretch in your knees with exception of pressure caused by the surrounding major muscles in contraction.
Regarding the confusion over the video in question: As Herzog said, there is not a muscle group known as hip abductors, just adductors, on the inside. However, there is the motion of Hip abduction, being the femur moving outside the medial plane of the body, opposite of adduction. This is primarily controlled by your glute muscles as opposed to a specific group of 'abductors'. That being said, the stretch in the video will target muscle flexibility of your glutes, psoas and iliacus, and improve your abduction flexibility - ability to do the splits, much more than it will target your hamstrings and adduction flexibility: ability to butterfly.