Multilib

There's a good tutorial (and packages) on how to set up multilib support (32-bit programs on Slackware64) at AlienBOB's site. You'd do well to go there next.

However, as that's not complete and clear on all points, here are some details:

Binary display drivers

You need to reinstall binary drivers. ATI and Nvidia driver packages contain both 64bit and 32bit libraries to be maximally useful on a 64bit multilib OS. However, the slackbuild scripts available at slackbuilds.org are not up to this task, so if you already installed 64-bit binary drivers from slackbuilds.org, you should remove these and then use ATI's or Nvidia's driver installer.