Actually, video editing uses very little video RAM. On the other hand, it will use as much system RAM as it can. When video editing, you only need as much video RAM as the video frame buffer will require. If you are working on high definition content (1920x1080), your video card needs about 64MB of RAM, it if it triple buffering.
Now, there are some utilites/programs for creating title screens and special video effects which do require a much better video card. Those are not considered "video editing" tools. They are "content creation" tools.