My question might be quite stupid but I have no idea how to do this and have tried everything I could. I just want it to do the same but over serial communication and not over a server/client.
That isn't a question. That is a statement.The ino file you posted gets data from the serial port. I don't understand what the problem is.
You need to provide links to this so it is known what kinect is.
I need to make this .ino file talk to the processing file to be interpreted by the Kinect Sensor.