To let your linux distribution run 32 bit executables,
you should install the standard and the most used libraries in their x86 form.

This is different from distrubution to distribution. Generally speaking,
you should use your package manager (for example, yum for fedora/centos,
apt-get for ubuntu/debian, etc.) to install the ia32-libs package.

You should be root to install those libraries.

Ubuntu 12.10 and pre-12.10:

sudo -i
apt-get update
apt-get install ia32-libs

Ubuntu post-12.10:
(in this version of ubuntu, they removed the ia32-libs package, so we should add
the package sources from the old release)

sudo -i
cd /etc/apt/sources.list.d
echo "deb http://old-releases.ubuntu.com/ubuntu/ raring main restricted universe multiverse" >ia32-libs-raring.list
apt-get update
apt-get install ia32-libs

Debian:

sudo dpkg --add-architecture i386
sudo apt-get update
sudo apt-get install libc6:i386
sudo apt-get install ia32-libs

Fedora:

su -c 'yum install --skip-broken arts.i686 audiofile.i686 bzip2-libs.i686 cairo.i686 cyrus-sasl-lib.i686 dbus-libs.i686 esound-libs.i686 fltk.i686 freeglut.i686 gtk2.i686 imlib.i686 lcms-libs.i686 lesstif.i686 libacl.i686 libao.i686 libattr.i686 libcap.i686 libdrm.i686 libexif.i686 libgnomecanvas.i686 libICE.i686 libieee1284.i686 libsigc++20.i686 libSM.i686 libtool-ltdl.i686 libusb.i686 libwmf.i686 libwmf-lite.i686 libX11.i686 libXau.i686 libXaw.i686 libXcomposite.i686 libXdamage.i686 libXdmcp.i686 libXext.i686 libXfixes.i686 libxkbfile.i686 libxml2.i686 libXmu.i686 libXp.i686 libXpm.i686 libXScrnSaver.i686 libxslt.i686 libXt.i686 libXtst.i686 libXv.i686 libXxf86vm.i686 lzo.i686 mesa-libGL.i686 mesa-libGLU.i686 nas-libs.i686 cdk.i686 openldap.i686 pam.i686 popt.i686 pulseaudio-libs.i686 sane-backends-libs.i686 SDL.i686 svgalib.i686 unixODBC.i686 zlib.i686 compat-expat1.i686 compat-libstdc++-33.i686 openal-soft.i686 redhat-lsb.i686 alsa-plugins-pulseaudio.i686 alsa-plugins-oss.i686 alsa-lib.i686 nspluginwrapper.i686 libXv.i686 libXScrnSaver.i686 qt.i686 qt-x11.i686 pulseaudio-libs.i686 pulseaudio-libs-glib2.i686 alsa-plugins-pulseaudio.i686 dbus-glib.i686 gtk2-engines.i686 libcanberra.i686 libcanberra-devel.i686 libcanberra-gtk2.i686 libcanberra-gtk3.i686 gtk-murrine-engine.i686 PackageKit-gtk3-module.i686 qtwebkit.i686'

To run the x86 version of Blockstorm you should modify the following file:
~/.steam/steam/SteamApps/common/Blockstorm/Blockstorm

This is the original file:

#!/usr/bin/env bash
GAMENAME="Blockstorm"
ARCH=`uname -m`
if [ "$ARCH" != "x86_64" ]; then
ARCH="x86"
fi
export LD_LIBRARY_PATH="./"$GAMENAME"_Data/Plugins/"$ARCH"/:$LD_LIBRARY_PATH"
exec "./"$GAMENAME"."$ARCH "$@"


modify the 3rd line in:
ARCH="x86"

then, Steam will run the 32 bit version of Blockstorm.