The background image is nearly identical to the default one in Kubuntu 13.04. And the icon artistry reminds of some of the older versions of Kubuntu / KDE, which makes me think it's in that family.
However, the rather purified look of the desktop widgets (menu bar, icons, etc.) reminds me more of Lubuntu.
Both KDE (used by Kubuntu) and LXDE (used by Lubuntu) are highly customizable desktop environments, so it could easily be either one of those, with heavy customizations applied to it.
It could also be one of the related distributions (that used KDE or LXDE). For instance, the "<icon> MENU" for the menu button makes me think of an early version of Peppermint OS (that uses LXDE). But it could also be some old version of Linux Mint (which has also had this button with "menu" spelled out), but Linux Mint looks a lot nicer than this, so it must be very old.
The childish look of the icons make me think a bit of PuppyLinux.
It's impossible to really be sure without any obvious marker that can be made out from the blurry picture (like the distro icon). And there are also many many Linux distributions, including some that are niche derivatives distros that were made just for a specific organization or purpose. So, I'm afraid I cannot narrow it down any more specifically than that.
Can you post a link to the original video? That might yield further clues!
It's definitely not one of the major distros (unless it has simply been heavily modified). And I agree with Mike the bottom bar definitely hints that the desktop could be Kde or lxde based. The dock on the left could be any of a number of dock apps/widgets.
Just from that one screenshot, it is really hard to tell what distro is installed on that machine!