She has never been identified, as far as I know. She was a regular announcer for TWC (her voice was also heard on promos from the late 80s until early 1990), either on staff or a freelancer. The "constant narration" you reference on the clip was only used for about six weeks or so before TWC scaled it back to the more familiar narration used from late 1987 until 1995. Dan Chandler also recorded narration during this period that was as verbose and constant.