EDIT: UPDATE: This is wrong. The xhost + wasn't the special sauce after all. So, don't do it. Running firefox (and presumably a number of other X applications might also work) before running EBII is the secret. The "BadAtom" error is likely happening because the atom does not exist. What I think is happening is that firefox creates it when it finds the atom missing. I'll see if I can figure out which Atom is causing the problem. Still, I have work-around.
EDIT: UPDATE 2: Yep. It's a non-existent atom, possibly a few, probably one or all of the NETWM atoms, as using a more modern WM works (so firefox and window maker both create the atoms EBII is looking for). The lesson? Use something at least slightly more feature-rich than twm. Slackware 13.1 32-bit works fine out of the box, unless you do something really silly.
If there is a bug here, it is in the BlitzMax backend code, which should either ignore the non-existent atoms, or it should create the atoms and move on. Again, only silly people who do stuff like run twm in the 21st century are going to run into this problem, so I wouldn't even be annoyed if the BlitzMax guys ignored it as a 'wontfix' bug.
ORIGINAL (WRONG) POST: Solved! It's a different problem on Slackware 13.1 32 bit than on the 64 bit with chroot jail. It's an Xwindows permissions problem. I'm not sure what permission precisely, but getting out the big hammer seemed to work:
This says, allow everyone! From anywhere! Don't do this unless you know what your doing! It opens up your X port all the way, and is not suggested for normal use. If I cannot get a finer grained command, I'm going to create a script which will lock down my X port (6000) with iptables before running this command and starting EBII.
I'll post any further findings here, whether it is a finer grained xhost command or the iptables script. This may be a little while. I'm hopping a plane on Sunday and will be out of town for the week.
Also, sound doesn't work, but Slackware doesn't ship with OpenAL (pretty simple download-compile-install though, I've done it for other games in the past). Also, I've got a funny audio setup (which the stock kernel doesn't handle correctly), but that's a recompile away. Otherwise, it seems to be running plenty fast. So, 13.0 is missing the correct libraries and 32 bit 13.1 has X locked down a bit too much. chroot jailing the 32-bit environment may or may not work for EBII, it certainly doesn't work with 13.0/64bit w/13.1/32bit chroot (tried and failed). We'll see what happens when I update my main system after I get back from my trip.
(Also, twm is ridiculous. No, I didn't bother setting up my normal X windows stuff, since I'm primarily going to be using the 64 bit install.)