He picked a Zener that has a little temperature coefficient, although the diodes will still have a negative tempco. As he explained in Part 2, this is intentional.

In this inventive twist on the Klon, Robert Keeley switches out the "mythical" diodes for germanium transistors and offers diodes as a switchable option, and there's a bass boost feature too ...

As an example, with a 12-V input, using a 2.5-V Zener diode would require a 1.9-kΩ series resistor to maintain 5 mA (assuming no load current).

I need a circuit to limit the voltage across some dissipation limited devices. It must: limit the voltage to a maximum of 1.5 V, have symmetrical limiting, be capable of accepting a current of 2 A, ...

In this inventive twist on the Klon, Robert Keeley switches out the "mythical" diodes for germanium transistors and offers diodes as a switchable option, and there's a bass boost feature too ...