There are plenty of reasons to use (and/or make) a ring light, especially for video:
+ Fill light - since the light is coming straight from the camera, it provides a nice wash of light pointed evenly at the subject. Like using a bounce or lanterns, ring lights can provide soft, diffused lighting.
+ Detail - if you're shooting something with lots of hard lights, ring lights provide a fill for the detail you may have lost in the shadows.
+ Halo shadow - If it's your only light, you'll get a "halo" of shadow outlining your subject (a signature ring light look).
+ Macro - shooting through a ring light provides perfect, even light from all sides of a small object.
+ Color effects - using different gels on different parts of a ring light creates color washes in all kinds of directions.
+ Catch Light - to see the stylized catch light in the subject's eyes, the camera needs to be pretty close. A bigger ring light means the catch light will show up from further away, but you also get a brighter, softer light!
https://vimeo.com/videoschool/lesson/312/the-many-uses-of-a-ring-light