So there is some concern with this system.
The HVAC is either on or off. It requires a certain airflow over the evaporator. If you close off enough of the dampers and choke airflow over the evaporator, it could freeze (literally).
Also, without conducting a study, I doubt that there will be any actual cost savings. Cutting off airflow to an unused room isn't going to make the HVAC system any more efficient. The HVAC system will be still on and pulling full power. You also run the coil icing risk mentioned above. Unoccupied rooms should be set to have the damper open.
Example: Only the master bedroom is occupied. The system heat/cools that specific room while the rest of the (large) house is uncontrolled and just gets hotter or colder overall. Then you exit the master and start moving through out the house. The HVAC will then need to kick on for an extended period of time to cool or heat the house. Plus the fact that the AC is running 100% no matter what dampers are open or close. So you are running a whole house AC to cool one room.
Edit: Yeah Linus really needs to read the YouTube comments. There are some serious concerns with the functionality of this system.