Stop flexing him toward your outside leg. By letting him flex in the opposite direction to where he is travelling, he is moving forward through that shoulder. Keep his head and body straight, and have a little resistance in your hands. Sit up straight and keep a lot fo weat in your seat, make sure your body is straight also. He should be able to side pass with his body straight. If anything, he can have a little flexion TOWARD were your going. Sit your outside (by outside I mean the side you are moving AWAY from) rein against his neck, and open your inside rein a LITTLE. This encourages the sideways motion. From what I saw in the video, he is only moving forward through that shoulder, so keeping him straight should stop the forward motion, but if he does go forward then half halt and try again.
Hope this helps, its what I did with my arab and he's pro at it now :]