Signal multiplication in AM transmitter circuit
What you have drawn shows how it is hooked up and does not show a proper circuit.

With some guessing I see how it can work though.

The supply voltage of the crystal oscillator is varied (modulated) and that gives very weak amplitude modulation because those changes in the oscillator's supply voltage will result in changes in the amplitude of the oscillator's output signal.

This is not a proper AM transmitter, it's a hack. For example, a proper AM transmitter would transmit a sinewave containing only one frequency, for example 1 MHz. This circuit outputs a square wave which means it outputs a whole bunch of frequencies, all the uneven multiples of 1 MHz. So it will transmit 1 MHz, 3 MHz, 5 MHz .... etc.

It's a "poor man's" circuit and behaves as such. Don't expect miracles from it and don't connect a long (efficient) antenna to it as you will disturb AM reception in your area.