Is there a technical reason why you might use a two inverting amplifiers instead of a single non-inverting amplifier?
The AD590 has a CURRENT output. For this reason, you must use an opamp wired as an (inverting) current-to-voltage converter - and you cannot (directly) feed a current into the noninverting input terminal of an opamp.

The mentioned gain of 1000 is a voltage gain (but your input signal is a current). Hence, in case of an ideal current source the input current I goes through the feedback resistor and produces a an output voltage of
 Vout=-I*R28.

If your question is a general one - independent on the shown example circuit, the answer is as follows: There are many cases where an inverting amplifier is required - for example as active devices in active filter circuits, harmonic oscillator circuits or as a controller block in control loops.