This is a non-intelligent differential sensor designed as a "bridge" circuit. (Very common with pressure sensors)
The two signals coming from the pressure transducer are usually attached to the inputs of a Instrumentation Amplifier (such as an INA122, a single supply device). This device would then connect to an analog input of the Arduino
The real issue you need to deal with that I see using this device is that it is a 3V device. Which means you need to have a 3V power source (not a big deal) and then scale it to send 0-5 to the Arduino. This means that you will need to do some calculations (see the INA22 datasheet) to figure out the right gain resistor to get the full scale readings you want.