The installation/performance in question: http://www.botndolly.com/box .
Bot and Dolly (the firm behind this performance/installation) will will apparently release a post-mortem at some point but here's a quick dissection of the tech.
A big part of this performance is video/projection mapping (mapping animations and graphics to physical objects that aren't necessarily a screen).
MadMapper (http://www.madmapper.com/) seems to be the app of choice to getting started with projection mapping really quickly is (it's expensive tho).