The circuit used is a type of collector resonance Royer oscillator which has the advantages of simplicity and self resonant operation. A very similar circuit is used in common inverter circuits used for powering fluorescent lighting such as LCD backlights. They drive a center tapped transformer which steps up the voltage to around 800V for powering the lights. In this DIY induction heater circuit the transformer consists of the work coil and the object to be heated.
The main disadvantage of this circuit is that a center tapped coil is needed which can be a little more tricky to wind than a common solenoid. The center tapped coil is needed so that we can create an AC field from a single DC supply and just two N-type transistors. The center of the coil is connected to the positive supply and then each end of the coil is alternately connected to ground by the transistors so that the current will flow back and forth in both directions.