More on the darlingtons later... but the output limit circuit can be guessed at. With the output fully shorted, on a half wave the voltage increases until the transistor chain turns on. There are 3 diode drops in the transistor chain, so approx 0.7*3 = 2.1V. The Zener conducts at 4.3V so it will shut down current to the output as soon as the difference (4.3 - 2.1) = 2.2V appears across the resistor. It does that by "stealing" the TIP120's base current. By Ohm's law, it would then set a current limit at 2.2A. Mainly, the current limit is to protect the 3055 from thermal runaway and destruction. One advantage over a PTC (comparing head to head functionality) is that it's instantly self resetting, it will return to normal after the short is removed. So an intermittent short like a points bridging, won't take down the power supply. You can change the 2.2A limit to anything you like by changing the Zener voltage or the 1 ohm resistor (but 1 ohms gives a good range, shouldn't be changed really...).
The reason you don't see much current in the Zener, I'm not sure, but you should see the current from the 220 ohm resistor. If you see absolutely no current, it's possible the Zener voltage on the virtual component is set way too high and it's just not conducting (at the same time, the current limiting would not be working at all).
This current limiting circuit was very common in hifi and other sound amplifiers in the 20th century. Sometimes they used a chain of diodes instead of a Zener, to save money.
The PTC itself isn't a bad idea, however since the circuit already has current limiting, some thought should go into choosing the right trip values for the PTC. In other words, pairing it with the output behaviour...