I tried to get it to run. It needs the newer glibc, as it will complain about being unable to find GLIBC_2.15XX in /lib/libc.
Anyways, looking at a package of Steam Linux from the Arch Linux Aur: The following dependencies are needed.
'bash' 'desktop-file-utils' 'hicolor-icon-theme' 'ttf-ms-fonts'
'libjpeg-turbo' 'curl' 'gnutls' 'libogg' 'pixman' 'sdl' 'libtheora' 'libvorbis' 'alsa-lib' 'glibc' 'cairo' 'libcups' 'dbus'
'fontconfig' 'freetype2' 'libgcrypt' 'gdk-pixbuf2' 'glib2' 'gtk2' 'nspr' 'nss' 'openal' 'pango' 'libpng12' 'libpulse'
'gcc-libs' 'libx11' 'libxext' 'libxfixes' 'libxi' 'libxrandr' 'libxrender' 'zlib'
Also, for each binary / game steam installs I'm sure you'll need to run brandelf -t linux.
So I'm guessing if you did get it to run, you'd need to make some sort of wrapper, that will automatically brandelf the binaries, and run them with the correct paths.