The video playback is only supported if the clip goes through the Windows display driver. If the playback is using the so-called video overlay technique, where the image/video is produced and displayed directly by your video card, then it cannot be captured. This also happens often with 3D games as well.
Some video files, like certain WMV playbacks, should show up in Remote Control. If possible, please try to change the format of your video playback to use Windows display if you wish to view the contents over LogMeIn.