GODDAMN 1 min edit limit.
What you should do is CFLAGS="-m32" LDFLAGS="-m32" make; sudo make install32. I just c&p the Makefile without looking at it again, and I thought I had added the -m32 flag in there. But apparently I set them as environment-variables.
And since I'm doing another post anyway, I might as well add this:
In case I'm wrong on that, you'll have to build mesa yourself, but that's not so hard as well. This:
And I'm not 100% sure, as I'm not a Ubuntu-user, but I think the xorg-edgers ppa already gives you 32bit mesa and drivers, so you should be clear on that front.
should do the trick. If you're missing any dependencies you should be able to install them via apt-get build-dep mesa. When you build mesa that way you'll need to prepend LIBGL_DRIVERS_PATH=~/src/mesa32/lib/gallium/ LD_LIBRARY_PATH=~/src/mesa32/lib/ (adjust the paths) to what you want to run.
git clone git://anongit.freedesktop.org/git/mesa/mesa
./autogen.sh --enable-32-bit --enable-gallium-radeon --disable-gallium-llvm --with-state-trackers=dri,glx,egl,vega --with-dri-drivers=r300,swrast
cp lib/gallium/radeong_dri.so lib/gallium/r300_dri.so