Had a look at the video... There's a little more here than meets the eye - just a little.
In that video there is a bracket mounted to the tripod screw in the base of the camera on to which is a side extension with a "cold shoe" mount, on to which an LED light is mounted. You can get the side mount extensions at many camera shops, or ebay (I'll post an example).
I'm going to add that in poor light, with a DSLR, you can often find that any off-set combined with obstruction to light paths from the camera or lens can lead to un-even lighting. If I'm using my Sony SLT-A77 for video where I can't set up external lights, I prefer to use my large powerful (98) LED ring light. The ring light generates a distinct look, but it's better than a moving flat panel.