You need to set your library path to mimic what steam.sh does as you need to check the Steam runtime.
Also, the newest dependency in Steam is likely libudev.so.0, but that's coming from steamclient.so, not steamui.so.
Issue has disappeared with latest update of steam client...
Nothing extracted yet.
After the latest steam client update the client fails to startup with 'Failed to load steamui.so'
Platform: ubuntu 12.04.3 LTS x86_64
OpenGL drivers: AMD Catalyst 13.11 beta6
To try to narrow the Issue down I have tried various older drivers. Steam client always fails in the same way. Using an older client configuration restoredfrom backup the client starts successfully until it self-updates at which point the failure recurs.
A quick ldd shows no obviously missing libraries.
as@mouldy:~/.local/share/Steam$ LD_LIBRARY_PATH=
pwd/ubuntu12_32:$LD_LIBRARY_PATH ldd ./ubuntu12_32/steamui.solinux-gate.so.1 => (0xf77cf000)
libcef.so => /home/as/.local/share/Steam/ubuntu12_32/libcef.so (0xf3810000)
liboverride.so => /home/as/.local/share/Steam/ubuntu12_32/liboverride.so (0xf3808000)
libsteam.so => /home/as/.local/share/Steam/ubuntu12_32/libsteam.so (0xf34c0000)
libtier0_s.so => /home/as/.local/share/Steam/ubuntu12_32/libtier0_s.so (0xf3490000)
libvstdlib_s.so => /home/as/.local/share/Steam/ubuntu12_32/libvstdlib_s.so (0xf3448000)
libSDL2-2.0.so.0 => /home/as/.local/share/Steam/ubuntu12_32/libSDL2-2.0.so.0 (0xf3360000)
libXrandr.so.2 => /usr/lib/i386-linux-gnu/libXrandr.so.2 (0xf3318000)
libXext.so.6 => /usr/lib/i386-linux-gnu/libXext.so.6 (0xf3300000)
libX11.so.6 => /usr/lib/i386-linux-gnu/libX11.so.6 (0xf31c8000)
libGL.so.1 => /usr/lib32/fglrx/libGL.so.1 (0xf3128000)
libpangoft2-1.0.so.0 => /usr/lib/i386-linux-gnu/libpangoft2-1.0.so.0 (0xf30f8000)
libpango-1.0.so.0 => /usr/lib/i386-linux-gnu/libpango-1.0.so.0 (0xf30a8000)
libfreetype.so.6 => /usr/lib/i386-linux-gnu/libfreetype.so.6 (0xf3008000)
libfontconfig.so.1 => /usr/lib/i386-linux-gnu/libfontconfig.so.1 (0xf2fd0000)
libgobject-2.0.so.0 => /usr/lib/i386-linux-gnu/libgobject-2.0.so.0 (0xf2f80000)
libglib-2.0.so.0 => /lib/i386-linux-gnu/libglib-2.0.so.0 (0xf2e80000)
libgio-2.0.so.0 => /usr/lib/i386-linux-gnu/libgio-2.0.so.0 (0xf2d28000)
libgtk-x11-2.0.so.0 => /usr/lib/i386-linux-gnu/libgtk-x11-2.0.so.0 (0xf28c0000)
librt.so.1 => /lib/i386-linux-gnu/librt.so.1 (0xf28b0000)
libpulse.so.0 => /usr/lib/i386-linux-gnu/libpulse.so.0 (0xf2860000)
libm.so.6 => /lib/i386-linux-gnu/libm.so.6 (0xf2830000)
libdl.so.2 => /lib/i386-linux-gnu/libdl.so.2 (0xf2828000)
libstdc++.so.6 => /usr/lib/i386-linux-gnu/libstdc++.so.6 (0xf2740000)
libpthread.so.0 => /lib/i386-linux-gnu/libpthread.so.0 (0xf2720000)
/lib/ld-linux.so.2 (0xf77d0000)
libc.so.6 => /lib/i386-linux-gnu/libc.so.6 (0xf2570000)
libgdk-x11-2.0.so.0 => /usr/lib/i386-linux-gnu/libgdk-x11-2.0.so.0 (0xf24c0000)
libpangocairo-1.0.so.0 => /usr/lib/i386-linux-gnu/libpangocairo-1.0.so.0 (0xf24b0000)
libgdk_pixbuf-2.0.so.0 => /usr/lib/i386-linux-gnu/libgdk_pixbuf-2.0.so.0 (0xf2488000)
libcairo.so.2 => /usr/lib/i386-linux-gnu/libcairo.so.2 (0xf23b8000)
libXi.so.6 => /usr/lib/i386-linux-gnu/libXi.so.6 (0xf23a8000)
libasound.so.2 => /usr/lib/i386-linux-gnu/libasound.so.2 (0xf22b0000)
libXrender.so.1 => /usr/lib/i386-linux-gnu/libXrender.so.1 (0xf22a0000)
libnss3.so => /usr/lib/i386-linux-gnu/libnss3.so (0xf2170000)
libnssutil3.so => /usr/lib/i386-linux-gnu/libnssutil3.so (0xf2148000)
libsmime3.so => /usr/lib/i386-linux-gnu/libsmime3.so (0xf2118000)
libplc4.so => /usr/lib/i386-linux-gnu/libplc4.so (0xf2110000)
libnspr4.so => /usr/lib/i386-linux-gnu/libnspr4.so (0xf20d0000)
libz.so.1 => /lib/i386-linux-gnu/libz.so.1 (0xf20b8000)
libdbus-1.so.3 => /lib/i386-linux-gnu/libdbus-1.so.3 (0xf2068000)
libpng12.so.0 => /lib/i386-linux-gnu/libpng12.so.0 (0xf2038000)
libXfixes.so.3 => /usr/lib/i386-linux-gnu/libXfixes.so.3 (0xf2030000)
libcups.so.2 => /usr/lib/i386-linux-gnu/libcups.so.2 (0xf1fd8000)
libgcrypt.so.11 => /lib/i386-linux-gnu/libgcrypt.so.11 (0xf1f50000)
libgcc_s.so.1 => /lib/i386-linux-gnu/libgcc_s.so.1 (0xf1f30000)
libXcursor.so.1 => /usr/lib/i386-linux-gnu/libXcursor.so.1 (0xf1f20000)
libXinerama.so.1 => /usr/lib/i386-linux-gnu/libXinerama.so.1 (0xf1f18000)
libXss.so.1 => /usr/lib/i386-linux-gnu/libXss.so.1 (0xf1f10000)
libXxf86vm.so.1 => /usr/lib/i386-linux-gnu/libXxf86vm.so.1 (0xf1f08000)
libxcb.so.1 => /usr/lib/i386-linux-gnu/libxcb.so.1 (0xf1ee0000)
libatiuki.so.1 => /usr/lib32/fglrx/libatiuki.so.1 (0xf1ec0000)
libgmodule-2.0.so.0 => /usr/lib/i386-linux-gnu/libgmodule-2.0.so.0 (0xf1eb8000)
libexpat.so.1 => /lib/i386-linux-gnu/libexpat.so.1 (0xf1e88000)
libffi.so.6 => /usr/lib/i386-linux-gnu/libffi.so.6 (0xf1e80000)
libpcre.so.3 => /lib/i386-linux-gnu/libpcre.so.3 (0xf1e40000)
libselinux.so.1 => /lib/i386-linux-gnu/libselinux.so.1 (0xf1e20000)
libresolv.so.2 => /lib/i386-linux-gnu/libresolv.so.2 (0xf1e08000)
libatk-1.0.so.0 => /usr/lib/i386-linux-gnu/libatk-1.0.so.0 (0xf1de8000)
libjson.so.0 => /usr/lib/i386-linux-gnu/libjson.so.0 (0xf1de0000)
libpulsecommon-1.1.so => /usr/lib/i386-linux-gnu/libpulsecommon-1.1.so (0xf1d78000)
libXcomposite.so.1 => /usr/lib/i386-linux-gnu/libXcomposite.so.1 (0xf1d70000)
libXdamage.so.1 => /usr/lib/i386-linux-gnu/libXdamage.so.1 (0xf1d68000)
libpixman-1.so.0 => /usr/lib/i386-linux-gnu/libpixman-1.so.0 (0xf1cd0000)
libxcb-shm.so.0 => /usr/lib/i386-linux-gnu/libxcb-shm.so.0 (0xf1cc8000)
libxcb-render.so.0 => /usr/lib/i386-linux-gnu/libxcb-render.so.0 (0xf1cb8000)
libplds4.so => /usr/lib/i386-linux-gnu/libplds4.so (0xf1cb0000)
libgssapi_krb5.so.2 => /usr/lib/i386-linux-gnu/libgssapi_krb5.so.2 (0xf1c70000)
libgnutls.so.26 => /usr/lib/i386-linux-gnu/libgnutls.so.26 (0xf1ba8000)
libavahi-common.so.3 => /usr/lib/i386-linux-gnu/libavahi-common.so.3 (0xf1b98000)
libavahi-client.so.3 => /usr/lib/i386-linux-gnu/libavahi-client.so.3 (0xf1b80000)
libgpg-error.so.0 => /lib/i386-linux-gnu/libgpg-error.so.0 (0xf1b78000)
libXau.so.6 => /usr/lib/i386-linux-gnu/libXau.so.6 (0xf1b70000)
libXdmcp.so.6 => /usr/lib/i386-linux-gnu/libXdmcp.so.6 (0xf1b68000)
libwrap.so.0 => /lib/i386-linux-gnu/libwrap.so.0 (0xf1b58000)
libsndfile.so.1 => /usr/lib/i386-linux-gnu/libsndfile.so.1 (0xf1ae0000)
libasyncns.so.0 => /usr/lib/i386-linux-gnu/libasyncns.so.0 (0xf1ad8000)
libkrb5.so.3 => /usr/lib/i386-linux-gnu/libkrb5.so.3 (0xf1a08000)
libk5crypto.so.3 => /usr/lib/i386-linux-gnu/libk5crypto.so.3 (0xf19e0000)
libcom_err.so.2 => /lib/i386-linux-gnu/libcom_err.so.2 (0xf19d8000)
libkrb5support.so.0 => /usr/lib/i386-linux-gnu/libkrb5support.so.0 (0xf19c8000)
libtasn1.so.3 => /usr/lib/i386-linux-gnu/libtasn1.so.3 (0xf19b0000)
libp11-kit.so.0 => /usr/lib/i386-linux-gnu/libp11-kit.so.0 (0xf1998000)
libnsl.so.1 => /lib/i386-linux-gnu/libnsl.so.1 (0xf1978000)
libFLAC.so.8 => /usr/lib/i386-linux-gnu/libFLAC.so.8 (0xf1928000)
libvorbisenc.so.2 => /usr/lib/i386-linux-gnu/libvorbisenc.so.2 (0xf17b0000)
libvorbis.so.0 => /usr/lib/i386-linux-gnu/libvorbis.so.0 (0xf1780000)
libogg.so.0 => /usr/lib/i386-linux-gnu/libogg.so.0 (0xf1778000)
libkeyutils.so.1 => /lib/i386-linux-gnu/libkeyutils.so.1 (0xf1770000)