Nicolas
I wasn't reading your question properly. So let me continue a bit.
1) if you want to feed information to the PC via serial communication
The Serial class in Arduino lib allows you to connect via serial link to the PC. In this case, the ATMega 328 in the Gamebuino is first in serial connection to the FT232 chip in the Gamebuino. The FT232 chip enumerates as a serial port USB device on the PC.
In this case, what you need is a program on the PC that communicates with the Com port created by the FT232. The problem is, as far as I understand, that you need to get this input into another program. If you want the input from this program to act as a "keyboard-like" device in Windows, I believe you then have to write a Windows device driver for your program. There exist some helpful programs that will allow you to transmit serial communication to a TCP/IP port, if that is of any help. I have used programs called Serproxy and Tinkerproxy to get serial from an Arduino to a Flash program running in Windows.
2) If you want a "real" USB HID device, that allows you to input text no matter where you are (web page, windows program etc), in the same way an USB barcode reader works
In this case the easiest solution is to get for example an Arduino Micro with Atmega32u4 chip which has built-in USB support. You can then program that chip to communicate with the Gamebuino through I2C and communicate towards the PC as a real HID device. However, in this scenario the question becomes whether there is any point in using the Gamebuino at all, as the Arduino Micro can probably handle the interface to your fingerprint reader or whatever you had in mind directly.
3) a Funky option, if you want to try something out just for kudos
There exists a cool program called GlovePie that can be used to bridge between different types of devices. There's too much to go into detail here but for example Wiimote to PC to Arduino, or for example IR head position sensor to PC mouse is completely doable.
As it happens, the Nunchuck connector in the Wiimote is a standard I2C connection. You could make the Gamebuino emulate Nunchuck (libraries exist but can bother to dig them out) connect it to a wiimote, and use BT over Glovepie to control the PC