The magnets now rotate around the coil and an emf is induced in the coil. The circuit being closed, induced current results. The power dissipated i^2R comes from the power used by the external agency to cause the change of flux, in this case rotation of the electromagnets. But if the loop is open and the induced emf cannot result in an induced current, how does the energy of the external agency appear in the circuit? Is the emf generated itself a way to store that energy which expresses itself when current flows? But if this were to be true, the emf should have kept on increasing as the external agency would continue to supply energy, but this is contrary to Faraday's law as the emf would increase only if the rate of rotation of magnets would increase. So, the crux is, where does the energy used to rotate the magnets go when the circuit is open?
If the loop is closed, the external agency will find that there is a force/torque on the magnets when they try to move/rotate them. They have to work against this force, and lose energy, which will finally be converted to electric energy in the circuit.
Now if the loop is kept open, the external agency will not feel this opposing force/torque when they try to move/rotate the magnets, and then no energy is lost.
We once did a similar experiment in our lab: A Stirling engine was connected to a generator through a belt. A large resistor was connected to the generator through a switch. When the switch is off, the circuit is open, and the engine runs smoothly at 300 RPM. EMF is generated by the generator, but no energy is lost in the circuit.
As soon as one turns the switch on, the resistor starts consuming energy, and the speed of the engine suddenly reduces to about 150 RPM, as now it has to apply much greater torque to rotate the generator.
The power produced by the engine still remains equal. The angular speed decreases as torque applied by the engine increases (Power = Torque $\cdot$ angular speed)