Since it is an FM transmitter, the modulation is FM, but also a little AM.
T2 forms a Colpitts oscillator, with the oscillating frequency depending on the LC components, but also on the internal capacitances of the transistor. The transistor capacitances are dependent on the DC bias point, and since the modulating signals alters the T2 bias, results a change in capacitances -> a change in oscillator frequency -> FM.
But since altering the bias also changes the gain of the stage, the stage may vary the output voltage -> AM.
A better idea for a serious (higher power) transmitter is to use a limitter after T2, and even better to modulate using a varactor.
Modulating by changing bias may lead to long term instability of the oscillator, but in a simple&fun transmitter there is no problem.