I looked at the chroot stuff... and it just said "then you build the kernel as usual". I never did that (installed Ubuntu from an iso), so I don't really know what to do. I'm not sure I'm Linuxy enough to accomplish any of these methods.
If you already have 64bit Ubuntu installed these commands should setup the needed chroot for you (replace trusty with precise everywhere if you want 12.04 instead of 14.04):
sudo apt-get install ubuntu-dev-tools
mk-sbuild --arch=i386 trusty # Currently, first time it needs to be executed twice, unfortunately, please comment if you know how to omit this.
mk-sbuild --arch=i386 trusty
# Allowing the same home folder to be used
echo "$HOME /home/$USER none rw,bind 0 0" | sudo tee -a /etc/schroot/sbuild/fstab
Then you can use the chroot with just
schroot -c trusty-i386
After that command you should be in the same home directory, but in a different ubuntu "installation", where you can install a completely different set of packages (well, in that case it will be the same set, but with different arch) and should be able to build the game with the same script you've used before. But notice that it won't have sudo by default, you'll have to manage it with another command, executed from the main system, not inside the chroot (using a different tab or TTY for that may be convenient):
sudo schroot -c source:trusty-i386 -u root
In my case the basic chroot took only 670 Mb of space:
$ sudo du -sh /var/lib/schroot/chroots/
670M /var/lib/schroot/chroots/
With default bash prompt settings ($PS1) you should easily differentiate between chroot and non-chroot sessions by a prefix in parentheses:
(trusty-i386)~ $
If you don't have 64bit Ubuntu installed yet, I'd recommend Lubuntu
http://cdimages.ubuntu.com/lubuntu/releases/trusty/release/ in this particular case, because it's still have a desktop UI but that takes much less resources.