For a 32bit programm you need 32bit mesa, including drivers.
If your distro doesn't provide you with a way to obtain 32bit-drivers you'll have to build them yourself. That's actually quite easy and only a few commands. Here's how I do it:
Now whenever you want to run a 32bit programm like wine just prepend LIBGL_DRIVERS_PATH=~/src/mesa32/lib/gallium/ LD_LIBRARY_PATH=~/src/mesa32/lib/ (adjust the path ofc) to your command.
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