The Artisteer designs all use overflow:hidden for the side content so anything that overflows the width of the column will not be shown (in most browsers). Putting the video player in a side column that is not wide enough for it is a bad choice in general but its no different if you put an image or anything else that is too wide, it will be clipped in an Artisteer design and it will throw off the layout in most other designs. Best to put it somewhere that it fits or make the column wider (which may be tricky with Artisteer designs).
Best,
Joe