I use a cheap (10€) HDMI to USB video grabber and a HDMI-Output conversion kit for the Gamboy Advance. There are kits for most consoles.
Gameboy Camera -> Gameboy Advance -> HDMI -> USB -> /dev/video0
I also recently saw a post on hackaday that did it with a microcontroller, IIRC. Those are probably just grabbing the raw analog signal from the Camera, though. So no on-screen user Interface.
@hk Nice, thanks for the advice! :)