Quick update. Dumping the raw h264 video from the quadcopter into a file is something I managed to do very soon once I got the "magic word" the quadcopter was expecting. The raw file has .h264 extension, which can be played by most software available. Still, it seems ffmpeg, vlc or gstreamer will fail to play it at the right framerate. One way I found to convert the raw .h264 into mp4 without reencoding (the quality of the video is bad enough without any reencoding) is by specifying the frame rate in ffmpeg:
$ ffmpeg -r 24 -f h264 -i dump1.h264 -c copy dump1.mp4
I'm not 100% sure the actual frame rate is 24 frames/second [EDIT: I first thought it was 15] but the length of the video this gives more or less matches the real duration of the recording that I logged.
The weight of the video is about 63kB/s.