It is indeed a Zener diode, used to regulate the supply voltage to the ICs instead of the voltage regulator chip shown in #6/ #7. It would be normal for it to become hot as it could be dissipating significant power, particularly as you are using the module at its maximum voltage of 24 V.
That said, I calculate it should be dissipating no more than 60 mW at most with that 1k5 resistor feeding it so it should not be hot. That resistor value does not quite make sense to me however.
I suggest you carefully measure the voltage across it.
This is merely in the DC regulation part of the circuit. Quit unrelated. 