I am running 14.1 64bit, and recently bought a few games to mess around with on steam and one that I run through wine (specifically, counter strike: source & HL2 on steam and EVE online through wine). Since my machine is 64 bit i followed alien's guide when installing multilibs, and both steam and wine seem to be working fine as I can run less graphical intensive/2D games on steam (FTL) and the installer for EVE online proceeded just fine on wine, starting up the game client afterwards.

The issue I am experiencing - in addition to a big performance hit that may or may not be related to the graphics issue - is that with both CS:S and EVE when I enter the game all I see is...
http://imgur.com/EydMIXO

I asked on ##slackware and was advised to install libtxc, but it did not resolve the issue. Any ideas?

Do you have a complete 32 bit mesa/video drivers setup as well, or are you expecting 64 bit to work? Wine is usually 32 bit still.