The "sway" is created by both YouTube and/or video editing software in an attempt to stabilize the video. When you have a shaky video, you can correct it to some extent in an editing software. I do not know if Roger does this or not. Most editing programs will crop the frame slightly, and shift and rotate the entire view screen to help control the movement.
YouTube will ask you when it completes processing a video upload if you would like to stabilize your video. Sometimes the video may actually be shaky, and sometimes the "algorithms" in YouTube will see a moving train and a still background and assume a shaky video. YouTube's program for correcting this problem is very bad about causing the video to "bend." It will stretch parts of the frame while keeping others normal, or shift pixel rows to keep things "still." This causes things like the sway seen here, which can sometimes be more distracting than the vibration in the camera.
Casey