The video backgrounds (some static, some animated) were shown on TWC's feed, just as the satellite forecast is now. The WeatherStar III simply showed text over a transparent background (to show TWC's feed) instead of generating its own blue or grey backgrounds.
These backgrounds were used in the mid-1980s, but were eventually discontinued for two reasons: it was sometimes hard to read the Star's text over some of the backgrounds (a couple of them were pretty funky and competed with the words), and TWC was ready to introduce its first satellite forecast (instead of a black screen or these video backgrounds): a non-stop loop of the text-based "Travel Cities Forecast".