I want to create a custom taxonomy page showing a list of subcategories

Assuming the name of your custom post type is “videos”, you can create a new template file in the themes directory called taxonomy-videos.php. If your custom post type’s permalinks are set up correctly this template will be rendered anytime the main query returns ‘videos’, so at ‘http://www.yoursite.com/videos‘.

In the template file you can start a loop and cycle through each post returned from the DB.