How does this current limiter work? - and why doesn't it?
Looks like there are a few connections missing.  The low side current must be drawn through the 50m\$\Omega\$ resistor or through a printed trace that does something similar. 

Here is a schematic (courtesy of this site)  that is very similar, though not exact. 

Note how the two LM358 inputs are connected, and of course the dual op-amp power supply is 5V and ground. 

Your board has a '431 for the reference and a real current sense resistor, but is otherwise likely very similar.