If you want to show the Plupper widget in a dialog mode (i.e. in a lightbox-like overlay), you will need to include any Javascript implementation of the overlay dialog (eg. Shadowbox media viewer) by yourself.
Try it here
<a id="plupperDialog" rel="shadowbox;height=320;width=650"
title="Chat with us" href="#">Chat With Us</a>
<script type="text/javascript"
src="https://static.plupper.com/js/plupper.js"></script>
<link href="shadowbox.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="shadowbox.js"></script>
<script type="text/javascript">
Shadowbox.init();