The Mobile Player (HTML) version of the gallery requires that all the gallery files are on the same domain or subdomain as the web page containing the gallery's JavaScript embedding code. This is due to the same-origin policy.

The paths within your gallery's embedding code (the path to the 'simpleviewer.js' file and the baseURL) are currently absolute and use the www.sieg.be subdomain.
If you go to your web site via www.sieg.be (i.e. using the 'www' subdomain), then you should see the gallery displayed on your mobile device.

A simple solution would be to use relative paths (rather than absolute paths) in your gallery's embedding code and the gallery will then be displayed on both sieg.be and www.sieg.be.
Try code such as the following:

<!--START SIMPLEVIEWER EMBED.-->
<script type="text/javascript" src="/Birds/svcore/js/simpleviewer.js"></script>
<script type="text/javascript">
var flashvars = {};
flashvars.baseURL = "/Birds/";
simpleviewer.ready(function () {
simpleviewer.load("sv-container", "100%", "100%", "313131", true, flashvars);
});
</script>
<div id="sv-container"></div>
<!-- END SIMPLEVIEWER EMBED -->

The leading slash in the code above denotes your root directory.