The MPX10DP does not have an amplifier inside. The output is the output of the internal wheatstone bridge. It is not even compensated for temperature.
This is the manufacturers page about the MPX10 series: nxp.com MPX10 series.
You need an instrumentation amplifier and perhaps a temperature compensation. The INA125 is an instrumentation amplifier. It was used in the past with the Arduino a lot. Nowadays, most sensors are digital, and the bare sensors with wheatstone bridge output are not used that often anymore.
When you connect both sensor outputs to two Arduino inputs (without amplifier), then the difference is 35mV for 10kPa. The resolution is in theory 5V / 1024. The overall accuracy for two analog inputs perhaps 9 bits, then you can measure the 10kPa in 3.5 steps (about 2 or 3 kPa resolution).
If you seriously want to use this specific sensor, and don't want to use extra hardware, then you might have a look at my question about the differential mode and gain that is possible with the Arduino Mega 2560 and Leonardo.
Or you could buy a pressure sensor with 0...5V output, that can be connected to the Arduino analog input. The tutorial you mentioned uses the MPX5010. That sensor has a amplifier inside and is temperature compensated. They are reliable and ratiometric with the 5V, therefor super easy to use. With a lot of averaging in the code, you can get a high (relative) accuracy.