Yes, the oscillator is Colpitts type with common base transistor amp. The output of the first stage changes the base bias of the osc transistor, thus slightly changing the equivalent capacitance of the transistor, thus changing the oscillator frequency (and the amplitude slightly, too).
BTW, I modeled the oscillator in LTSpice for fun. The output impedance of the model is 700-j200 at 100 MHz. You can use that as a starting point to match the oscillator to 50 ohms using a conjugate matching network and expect about 1.5 mW output power, and its stable (for wideband FM operation, anyway) . If the matching network you use has a DC path to ground at its input (such as through an inductance and/or resistance), use a 10n or larger capacitor between the output of the oscillator and the matching network to block DC.