Once validated, you just need to update the post meta with the form input:
if ( url_allowed( $_POST['video-url'] ) ) {
update_post_meta( $post_id, 'video-url', esc_url( $_POST['video-url'] ) );
} else {
//if user edits entry to remove a url from input, it will be deleted
delete_post_meta( $post_id, 'video-url' );
}
If you look at the source of esc_url(), you can see it is using wp_allowed_protocols and wp_kses_normalize_entities().
Side Note:
It is also parsing the url with wp_parse_url(), a wrapper for php’s parse_url(), to check the different parts. Not unlike what we did in the url_allowed() function (in fact I’ll update that answer to use wp_parse_url() if you want).