Easy one first:
One more question: How does this circuit relate to a chopper circuit?
Unrelated. The chopper chops, i.e., there's some kind of control that turns a switch (e.g. a transistor) on and off. There's nothing like that in here, it's not a switch-mode power supply.
I don't understand why the voltage drops.
The current through a diode grows very quickly if you increase the voltage after you've crossed the breakdown voltage. A little more voltage, way, way, way more current.
Way, way, way more current has to come from somewhere: it must flow through your orange resistor. That means way, way, way more voltage drop across that resistor, so that the voltage across the zener doesn't increase very much. That's the "regulated voltage".
(It's not a great regulator. If I see a design where anyone uses this, unless it's a very special case, it's probably a very bad design. Don't do this in the wild, there's always a better way. All the circuits on the page you've linked to have been obsolete since ca the early 1970's. Also, they are colorized scanned photocopies of photocopies of copies from copies ... maybe find a better source for schematics, honestly.)
There is a current limiting resistor stopping the input source from being overburdened and if there wasn't that would be a short circuit.
Well, that resistor is half of the regulating mechanic, the other half being the Zener diode.