Yes both Zeners are matched and yes two parallel diodes will have lower ESR or dynamic differential resistance BUT ONLY IF THE SHARED current is well below the knee or well ABOVE the knee/
Two zeners in parallel will actually be worse than one Zener if he operated at the knee of 5mA as the shared current of 2.5mA increases the ESR by more than double negating the advantage of parallel.
Instead of using only 1.2mA and then using another diode with 270Ω for current limiting, had he changed the bias resistor from 2.2K to 470Ω for either the White LED or athe dual Zeners would out perform both Zeners for Load regulation or ESR. But then there is a 100mA limit on the L05 and power dissipation may also become a problem.
He would have been better off with lower ESR 7805 rather than an 78L05 and avoid the need for the zeners.
Rule of THumb. Use zeners or LEDs at >15% of rated current Minimum for good regulation. But still not as good as programmable Zeners using band-gap diode with Opamp.
Now let's compare a typical White LED rated for 20mA ( some are better (15Ω) & some are worse)
Because the designer chose to use an Integrator to regulate current limiting ANY drop in L05 Voltage from 220Ω diode load makes it wildly sensitive to mV variation in reference voltage. A drop in reference from L05 is due to its output ESR and the load from the current limiter diode going ON would be like an increase in Current sense voltage, THUS you have a positive feedback loop, causing it to have hysteresis and oscillate like a relaxation oscillator, THATS WHY he used two stages of regulation . It will still work but "motor-boat a bit" .. (read oscillate or porpoise)
IN CONCLUSION
It is important to understand Load regulation or current limit regulation is the ratio of source ESR to load variation of ESR ratio and if you want 2% load regulation make the source <2% of load variation. ( or 2% of full load if needed)
In this case two zeners at 300Ω ESR= 150Ω supplies voltage from 1.2K bias which improves
supply regulation of L05 by 1200/150 =8x better due to load regulation problem on 78L05. The variation from Current limiting diode via 270Ω is the main issue. . Of course the OA could have been supplied by unregulated Voltage rather than load the 78L05.
Load regulation of 78L05 is in spec as follows;
ΔVO Load Regulation
1mA ≤ IO ≤ 100mA 20typ 60max [mV] means ESR = 0.2typ. 0.6max [Ω]
1mA ≤ IO ≤ 40mA 5typ 30max [mV] means ESR = 0.12typ. 0.75max [Ω]
and with 20mA switched diode current that translates into 0.02A x 0.75Ω =15 mV worst case ripple which evidently required better regulation using the zeners, again due to Integrator and positive feedback loop.
The 7805 has an output resistance of 8 mΩ typ which is 15x bettertyp.