The circuit consists of two parts:

One is the LC resonant circuit formed by L1 and C1. The power oscillating between inductor and capacitor is much higher than the current drawn from the power supply. Therefore the dominating current waveform is a sinewave.

The second part is the centre tapped inductor and both mosfets. Its only purpose is to replenish the energy lost in the LC tank circuit. Assuming a large L2, the current flowing here is almost a square wave, alternating the current between both halves.

If you add both currents (from the LC tank and from the mosfets) together you have the current in both halves of L1.

Simulating the circuit and looking at all currents simultaneously is probably the best way for understanding this circuit.