If one wants a voltage output (e.g. to connect an external DMM, e.g. for logging) and the analog meter ouput it makes sense to have an extra OP to drive the analog movement this way.
The resistor from ground to the meter set the gain. So the 10 Ohms shown in the link would give 1 mA for 10 mV input voltage. For a 100 µA movement and 100 mV full scale range one would need some 1 K for the scale factor.
Usually the meter movements can stand something like 500% overload. So the protection does not have to be very accurate.
Some movements need/want a parallel capacitor for damping. A small cap in parallel (or directly from the OPs ouput to inverting input) may be needed for stability of the OPs FB loop.
A sufficient series resistor and than directly from the LTC1050 would also be possible - especially if the ouput full scale range is relatively large, like +-1 V.