That shows me the how, which I understood.
It doesn't explain anything about the why.
A resistor is normally used with a diode if you want to more rapidly stop the inductive current than a diode alone would.
In this case you have the opposite, you want to keep the fan current flowing when the PWM voltage goes low, so you don't want the resistor.
It similar to the inductor and free-wheeling diode in a switching regulator.
You want to keep the inductor current flowing efficiently when the transistor is off so you use a diode with as low a forward drop and resistance as practical.