Frequency of an LC oscillator is inherently unstable. If you vary the
9V supply, the frequency will change. If you change the load (antenna
length, in this example), frequency will change.
As the audio is applied to the base of the oscillator transistor, its bias
will change and its current will change, which leads to change of
interelectrode capacitance values: Cbc, Cbe, etc.
You may consider the capacitor between Collector and Emitter is the
feedback element.
Regards,
S. H.