With the components shown this circuit only produces about 3.5kHz, not the 'approximately' 455.5kHz claimed by the designer. I built it on a breadboard it using a uA555, then removed the 0.002uF capacitor to get the highest possible frequency, which was ~670kHz with the pot wound down to ground.
Here is the waveform at pin 3 captured on my oscilloscope:-
Without an external capacitor the waveform is highly asymmetrical because it is timed by stray capacitances in the wiring and inside the uA555. The rectangular wave has fast rising and falling edges, so it produces hundreds of even and odd harmonics up to the FM broadcast band and beyond. The signal can be tuned in at many places in the band.
I fed a 1kHz audio frequency tone into the 555's control pin, and it was clearly picked by an FM radio placed next to the circuit. I then hooked a 30cm piece of wire up to pin 3 to act as an antenna, and was able to receive a strong signal from the next room.
The optimum length for a 'whip' antenna is ~1/4 of the wavelength, which for the FM broadcast band is 2.78m (at 108MHz) to 3.41m (at 88MHz) so 750mm is commonly used. This would tune out the lower and higher harmonics to some extent, but to reduce interference at other frequencies to an acceptable level you would need to put a narrow-band tuned circuit between the 555 and antenna.
While this circuit does 'work', its poor frequency stability, reliance on parasitic capacitance and internal delays in the 555 (which could vary depending on the manufacturer), weak output and production of many unwanted harmonics makes it no more than a crude demonstration of FM radio transmission. In most countries it is probably illegal due to the massive amount of interference it puts out. There are many simple FM transmitter designs that are much better than this one - don't use it!