There is no specific voltage gain as such. It's really a current to voltage loop gain The circuit you posted is not equivalent to the circuit in the voltage regulator. Your circuit has no feedback, giving it a gain equal to the op amp open loop gain. My circuit is a closed loop, with negative feedback from the voltage across the shunt resistor, due to the current, to the gate of the MOSFET which controls the current.
The diode is to prevent the op amp output from affecting the MOSFET control voltage when the current is below the limit and the op amp output is at zero volts. The diode forward drop is inside the feedback loop so its effective voltage is reduced by the open loop gain of the op amp, and becomes negligible.
So basically you have two control loops. The voltage feedback controls the loop below the current limit point, and the current feedback loop controls the loop when at the current limit.