As Guy suspected, they're using the screen width to determine which set of controls to display, either 'desktop' or 'mobile'. The cut-off width is 768px. For those of you using iPads, the controls you see may depend on whether you're using the iPad in portrait or landscape.
For those of us on desktops & laptops, there is a way of hiding the 'filmstrip' using some custom styles, although it generally requires the use of an extension to apply custom styles.
I'm using a small bit of custom styling to push the filmstrip off screen, leaving only the buttons on view; see attached. And another bit of custom styling to restore the filmstrip on mousing over the buttons. I'm also hiding the 'information buttons', because they're pointless.
If anyone wants to know what extension I'm using and the custom styles I'm using, just say, and I'll explain it in detail. It's quite simple though.