From the datasheet, I have found that there is a signal for each pressure, ...
I think you have misunderstood the datasheet. The sensor is available in three versions.

- The single-port versions have the port exposed to atmosphere and the pressure differential is relative to the pressure in the sealed port (presumably some gas sealed into the device).
- The dual port version has each side exposed to a port.
... so can I obtain the reading of each pressure value alone from the instrumentation amplifier?
No, the dual port sensor has no internal reference pressure. Imagine the use case where it is being used to monitor the pressure drop across an air filter in a pressurised line:
- Port 1: upstream measurement pressure = 2 bar.
- Port 2: downstream measurement pressure = 1.7 bar.
- Pressure differential: 0.3 bar.
The sensor will be able to report the pressure difference but cannot give the absolute pressure (pressure above 0 bar) or the gauge pressure (pressure above 1 bar) as there is no reference signal available.

Figure 1. The sensing element appears to be a Wheatstone bridge device.
The differential signal is probably derived from a Wheatstone bridge circuit. Differential output allows the device to handle positive or negative pressure differentials while powering the device on a single rail supply.