You have a custom post type called ‘video’ with a video_url field. You need to call register_post_meta in the rest_api_init hook to get the API to return this field, e.g.
function register_post_meta_video_video_url( $wp_rest_server ) {
register_post_meta( 'video', 'video_url', array(
'type' => 'string',
'description' => 'Featured video URL',
'single' => true,
'show_in_rest' => true,
) );
};
add_action( 'rest_api_init', 'register_post_meta_video_video_url', 10, 1 );