Collpits FM Receiver

Question

I saw this simple schematic for an FM receiver:
https://www.mikroe.com/ebooks/radio-receivers-from-crystal-set-to-stereo/the-simplest-fm-receiver
Moreover, I saw some videos online where people have built it successfully:
https://www.youtube.com/watch?v=h_F3J4vyzNk
Starting at 2:58 on the video timeline.

I'm very puzzled as to how this circuit works. It's not mentioned in any electronic comm. texts, even as it's surprisingly simple for a circuit that successfully performs FM reception, filtering and demodulation.

I understand there is a Collpits oscillator at the heart of it that's tuned to the frequency of the station you want to filter, but that's where my understanding ends.

How does it turn frequency into voltage across the load resistor (R1) (schematic in the first link above) ?

I don't mind about the debiasing and audio amplification portion, as these I understand. What I don't know is how it's converting frequency into voltage at R1 ?

This circuit was demoed in several Youtube videos, but the operating mechanism is never simply explained. Maybe they understand it so well that they forget that an explanation is needful..

Here's an explanation for a different kind of FM demodulator, and it'd be great if this circuit could also be explained in the simple style of the explanation below:

My simple explanation for a FM Monostable Multivibrator demodulator:

1. A multivibrator produces a voltage "tick" for every peak of the sinusodial waveform, so higher frequency produces more ticks and vice versa.
2. When the voltage rectangles coming out of the multivibrator are loaded with a low pass filter, a greater voltage will be seen across the capacitor for denser multivib output and vice versa.
3. So higher frequency --> denser multivib output --> higher voltage across lowpass filter, which is a biased form of the audio voltage behind the modulated signal.

EDITS

People kindly pointed out that the LC tank's amplitude varies with the frequency.

But why have an oscillator in the first place if all we need is a slope detecting LC tank ? (A slope detecting LC tank + a diode envelope detector to filter out the carrier). Why bother with a Collpits oscillator ? Moreover, what filters out the carrier after the LC tank varied the amplitude ?

Answer 1

Even a very small signal fed into an oscillating circuit can cause it to lock to the incoming signal (Injection locking.) This is exploited in this circuit where the oscillation frequency follows that of the incoming signal.

As the oscillation frequency varies and moves away from the resonance frequency of the tuned circuit the amplitude will tend to fall, which in turn cause the supply current of the circuit to change - this results in the audio signal appearing at the headphone. (Slope Demodulation). This is a result of the transistor rectifying the oscillations and altering the bias point of the circuit.

This type of circuit, although simple, has many disadvantages and so is rarely used in serious designs.

There's a paper about the operation at https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6774035, unfortunately behind a paywall.