The 1mOhm shunt resistor is much smaller than usual, which leads to very small voltage levels.
The max NES-350-48 current of 7.3A would lead to only 7mV which means that component variation (especially DC offset in the opamp) are significant and you need at minimum a trim pot to set the input at the right level to compensate for that and choose the actual current limit, because most opamps have at least 2mV DC offset variation (may be larger over temp) so the 1mOhm shunt would make your current limit uncertain by 2A, in other words, it could limit at 5A or at 9A, which is quite a large variation. Normally shunts are 5mOhm like in Richard's design and deliver 35mV drop at 7A which is much better manageable.
Op amp gain is 600 (60k/100) so the output reaches approximately 4.2V when max current is reached (assuming 7A).
Why not drive the OVP directly from the opamp output through a diode so you can only lower the NES output voltage at current limit?
Most opamps (not all) can deliver 1 mA and the OVP point has about 1mA current flow in the NES, so you can pull hard enough with just the opamp.
In case the opamp cannot *source* current, only sink, then it only needs a resistor from the opamp output to the + supply line.
Why use 5V? The opamp can run directly from the NES 12V regulator.
With 5mOhm shunt and 7A current limit you need about 90x gain to get 3.1V from the opamp. Tie a 10k resistor from opamp output to +12V supply to make sure it can source 1mA and put a diode between opamp output and OVP point.
I did not build this circuit yet but this is how I would expect that current can be limited to 7A.
Whether it works or not, if you build it you get the guinea pig award
Note that if you look at Richard's limiter design, you will recognise a lot of this...