No route found for custom REST resource
As far as I can see, the REST UI module is just thought to change the content of the YAML files for the REST resources. It is up to the module correctly define the URL to use.

In your case, the annotation of the class should contains:

 uri_paths = {
   "canonical" = "/videos/feed/{site}",
   "https://www.drupal.org/link-relations/create" = "/videos/feed"
 }


I am not sure the placeholder makes any difference, but all the examples use {id}.