On one of these forums a few years ago, somebody complained that an FM transmitter circuit similar to the one you found did not work. It had the same problems as the one you found plus its audio preamp transistor was incorrectly biased so did not work (it was saturated) when the battery was new at 9.4V and also failed (it was cutoff) when the battery voltage dropped to 7V after being used a little.
I built the faulty circuit and confirmed the bias problem and improved the circuit with added modifications:
1) Adding an RF amplifier at the output so that things moving near the antenna did not affect the frequency and also increased the range.
2) Added a 5V low-dropout voltage regulator so that the frequency did not change as the battery voltage dropped, and so the preamp transistor kept its biasing.
3) Added pre-emphasis (treble frequencies boost) like all FM radio stations have so that the signal sounds perfect.
I built my FM transmitter compactly on Veroboard (stripboard). I tested it around my neighbourhood for only one hour because it was powerful enough to cause interference on the frequency it shared with a low power foreign language FM radio station on the other side of my city because my FM dial is full of stations.
It is mono, not stereo. If I want a stereo FM transmitter then i would make The Micromitter project that was shown in Silicon Chip magazine or build its kit.
Its range is more than 2km across a large river valley to my very sensitive home stereo and car radio. The radio station sharing its frequency reduced its range a little.
Its range is about 400m to my cheap Sony Walkman stereo radio.
Its range is across the street to a cheap FM scanning radio from The Dollar Store.
Houses and hills reduced its range.