How is an incandescent light bulb used for gain stabilisation?
As the amplitude increases, so does the power dissipated in the filament
This raises the filament temperature, hence its resistance, which is arranged so as to reduce the gain, thus stabilising the amplitude automatically.

Why choose a lamp instead of another non-linear resistor (voltage variable resistor) like a JFET or something involving diodes?

What's great about the lamp is that its resistance changes slowly, from the thermal inertia of the filament. Thus the resistance isn't varying to any great extent throughout the sinewave cycle, changing the gain during each cycle, which would add harmonic distortion to the waveform.

So lamp-stabilised Wien bridge oscillators tend to be used where low harmonic distortion is required. 0.01% or 0.003% (-80dB to -90dB) are quite easily achieved; lower THD is possible with care.

(At low frequencies, as the period approaches the filament's thermal time constant, you can see gain decreasing at the peaks of the waveform, in the form of 3rd harmonic distortion).

Thermistors have similar characteristics, and are sometimes used - but the gain has some dependency on ambient temperature too.