Something like that would most likely be run using a system like watchout - which is a linear timeline based playback system and the cues would all be regular "go" cues to advance between pause points on the timeline. It would be much like a dance, where timing and blocking is crucial on the actors part because you cannot adjust the projections on the fly.
It was hard to tell from the clip whether there is orchestration involved - but if there was any live music, normally you would place click inside the playback program - and often any of the "fill" music as well. If it was all playback, then everything would sit inside the video playback program to ensure that the music timing and projection matched 100%.
The biggest problem with interacting with projection is the fact that live theatre can start to be a lot less "live" due to the rigid nature of projections. It is something that Cirque du Soliel and a number of other innovative companies are really keen on experimenting with using various sensors and motion capture systems to make projection dynamic.
