zip download plugin works well in localhost but not on live site

As you can see, the code of the linked question add a custom gallery shortcode in this function:

private final function __construct() {
    remove_shortcode( 'gallery' );
    add_shortcode( 'gallery', array( __CLASS__, 'gallery_zip_shortcode' ) );
}

and then this custom gallery shortcode is executed in this function:

public static function gallery_zip_shortcode( $atts ) {

    $post = get_post();

    if ( ! function_exists( 'gallery_shortcode' ) )
        require_once ABSPATH . 'wp-includes/media.php';

    self::get_gallery_images_from_shortcode( $post->ID, $atts );
    $output = gallery_shortcode( $atts );

    $gallery_id = count( self::$images[$post->ID] ) - 1;

    $link = sprintf( '<div><a href="#" gallery-id="%d" post-id="%d" class="gallery-zip">%s</a></div>', $gallery_id, $post->ID, __( 'Get as Zip' ) );
    $output .= $link;

    return $output;

}

Try to comment out the $output = gallery_shortcode( $atts ); line.

The other issue (which you forgot to mention in your question) about the download link not working is because the plugin can have unexpected behavior, as it actullay is, for WordPress < 3.5. You should contact the developer.

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