Hello,
I actually found where the error came from.
I was using an OpenNI folder from another camera installation, hence some packages were broken.
How to fix : Download OpenNI from the official website : OpenNI 2 Downloads and Documentation | The Structure Sensor
Install it, then go to the installed folder (which should be in Program Files). Then in OpenNI2\Redist\OpenNI2\Drivers, copy paste the two driver files that you will find in the SDK folder that you can download from the orbbec website. In this specific location : \Windows\Astra OpenNI2 Development Instruction(x86)_V1.3\OpenNI2\OpenNI-Windows-x86-2.3.0.55\Redist\OpenNI2\Drivers copy the two Orbbec and orbbec.dll to the previous mentioned path.
From this point your application should find the camera.