How is power to an entire room restored by plugging something into an outlet in an adjacent room?
Most likely scenario is that all the devices in the "dead room" are daisy chain wired on the same circuit coming from the outlet that you plugged the printer into. That printer outlet is likely to have been wired up using the notoriously unreliable back stab connections on the outlet. One of the back stab connections has come loose and when you plug in the printer it torques the contact metal inside the outlet just enough to make the loose wire connect up again. 

The loose wire in the back of the "printer outlet" could be the source of arcing and this can build up heat and maybe become a fire danger. It is wise to get this addressed as quickly as possible. 

When the circuits are repaired make sure to have all the wires be secured by the side screws on the outlet. That will give you reliable connections for years to come.