There is a ambiguity, on picture they install IRF510 or IRF520 MOSFET,
as you can see marking "FET" on the body of the transistor.
And FET doesn't require resistor, as no DC current.
It bad practice, IMHO resistor has to be any way, to limit
charging gate-source capacitor current.
On low frequencies arduino will survive such mistreatment at least.
But in description to the picture:
"Connect the base to an output pin of the microcontroller, and the emitter to ground like so: "
That is WRONG.,
If transistor is MOSFET, description must be:
"Connect the GATE to an output pin of the microcontroller, and the SOURCE to ground like so: "
if transistor TIP120, you already know what to do -):