Difference amplifier with current output error budget
I really don't understand the rightmost circuit. Where is the feedback
  path?


You have to consider the voltages on the op-amp's inputs and realize (as in all linear op-amp circuits) that they have to be equal (for an ideal op-amp). For this to happen (when current flows through the 0.1 ohm shunt resistor), negative feedback ensures the same volt drop across the 1 kohm resistor i.e. the op-amp output drops a little to turn on the PNP BJT and dump current through the 20 kohm resistor.

So if 1A is flowing through 0.1 ohms causing a volt drop of 0.1 volts then there also has to be a 0.1 volt drop across the 1 kohm. This means a current through the 1 kohm of 100 uA.

You can probably see immediately that the ratio of the two resistor values is inversely the ratio of the two currents.

The 100 uA (minus a tiny amount that flows through the base emitter junction) also flows through the 20 kohms. This means that with 1 A flowing to the power load, 2 volts appears across the 20 kohm resistor.

A PMOS would work more effectively in that there is no base current. Also, don't forget that the op-amp positive power rail has to be higher than 12V unless you are specifically using an op-amp designed for high-side sensing.