Hi razolgal,
we've just released a new version of the Responsive Background Slider, this version fixes the z-index issue.
You should donwload and install this latest version.
Additionally, your template uses a main div container (ID #art-main) which has position: relative; , this container has a black background (#000). You should set the background color of this div to transparent, or the eXtro Background Slider won't be visible.
maike