NascentOxygen said:
There are plenty of circuits, ...
I am afraid that circuit uses a discrete crystal, which is quite different to a crystal oscillator module.
A crystal is a resonator with a very high Q, typically about 1 million. What can be done with a crystal is decided by the external circuit.
A crystal oscillator module is designed to be extremely stable in frequency. Crystal oscillator modules have insufficient bandwidth, or external frequency adjustment, to allow audio FM modulation. Oscillator modules usually produce a clock signal, which is a rectangular wave with high harmonic content.
A voltage controlled oscillator, VCO, is designed to be frequency modulated by an external voltage.
A good engineer can design a crystal oscillator that dampens the high Q of a crystal, which can then be FM modulated. That makes a VCO and defeats the reason a high Q crystal was used in the first place.
The circuit you provided uses that technique to generate an FM signal.