Thank you all @DVDdoug @jremington @Devanshu_Acharya for your thoughts! Much appreciated. I just saw that the pic I uploaded in my first post was not the final version. Pardon me.
Here is the circuit with all the data (the Zener circuit is unchanged):
The Zener voltage is in all cases just above the total voltage an 8 LED string draws. So I guess it at least protects them from voltage spikes (explanation 3).
But how about explanation 1 and 2? If true, does the Zener protect anything and how does it achieve that?