Hi,
It seems that the issue is linked to your SSL setup and your template.
If you access that same page with HTTPS instead of HTTP in the URL, then all the URLs of the resources (javascript, CSS, etc) will use HTTPS and the shadowbox buttons will work fine.
I would recommend you always use HTTPS. Not only it will fix that problem, it will also be better for your SEO and the security of your customers data.
Joomla has a setting you can activate for that:
docs.joomla.org/Enabling_HTTPS_on_your_site