After searching the web for a few tips and tricks, I finally managed to make it run.
- Install the i386 architecture (sudo apt-get install libc6:i386)
- Install the default debian package from the Steam website (http://store.steampowered.com/about/)
- Create a small script to launch Steam
LD_PRELOAD='/usr/$LIB/libstdc++.so.6' DISPLAY=:0 steam
- Make the script executable: chmod +x Steam.sh
- Execute your script
It's sad that we need to apply this workaround until the Steam team does provide a better package, but it does work.