You can see the Video.js Playlist UI plugin in action below. Look at the source of this page to see how to use it with your videos.
In the default configuration, the plugin looks for the first element that has the class "vjs-playlist" and uses that as a container for the list.
When using the `horizontal` option, you'll want to set a width on the "vjs-playlist" element (or the class that gets added, "vjs-playlist-horizontal").