The reference design is total nonsense, forget it now!
The idea of class C is that you drive the transistor between two states, completely shut off and fully saturated. Obviously you get extremely high distortion when you do this but you don't use class C in linear applications anyway. In both states the power dissipated in the transistor is close to zero, in the off condition Ic is zero and in the on condition Vc is zero (it's really VCEsat but that's very small). As the transistor dissipates Vc * Ic Watts, in both cases it is almost nothing. Power is only wasted during the transition from on to off and back again.
If you ran it in class B, in other words with zero bias, there would be a longer rise and fall period during the cycle. During these periods the transistor would be partially conducting and generating heat.
In class C you deliberately force the transistor to be off until the input cycle exceeds the transistors Vbe and the reverse bias voltage you apply. This discharges the base capacitance quicker and also reduces the portion of cycle in which the transistor conducts. Essentially, you get a faster turn-on and faster turn off so the transistor spend less time partially conducting and keeps cooler.
Now the problem is the collector voltage/current is no longer anything like the input waveform, it is distorted to a square(ish) wave, typically only one third of the original input cycle appears at the output and it abruptly changes from zero to supply voltage. This is where the tuned circuit come in to play.
If you parallel a capacitor and an inductor you form a tuned circuit. If you pulse a voltage across a tuned circuit, it oscillates as magnetic fields in the inductor and electrostatic fields in the capacitor transfer energy to each other. The constant square wave pulsing from the transistor maintains the oscillation to produce your output waveform.
As for signal biasing, forget the rest of the transistor and just consider the base to emitter junction. It behaves like a diode and rectifies the signal, charging the capacitor as it does so. The resulting voltage is the the reverse bias needed to keep the transistor in class C condition. You can still provide your own voltage as well of course and most amplifier designs do just that.
Brian.