They say the processing was done in DP, but the visual graphics in the clip come from a combination of screen capture(s) and image editing software:
This video was made with image editing software and a screen capture program for the visuals, and a DAW (Digital Performer 4.5) to process the audio.
When you see the original wave form, and then the 'louder' wave form, they are clearly just zooming in at first, and then appear to show a compressed/limited wave form after when they compare where the louder peaks would have been. I believe they would have used either the limiter plug-in, or a combination of the compressor and limiter plug-ins to create the 'louder' wave form. But, from what they show in the video, there is no way to tell what they actually did.