>>editing<<
ah, found the entry you quoted...  

got it running?
there should be a.cfg file somewhere in the gamefolder..edit this line.
seta r_texturebits "32"
--> set to 16

Yes, this is the entire message:

CoD Beta build win-x86 Sep  3 2003
----- FS_Startup -----
Current language: english
Current search path:
C:\Archivos de programa\Call of Duty Dawnville Demo\main\pak0.pk3 (3208 files)
C:\Archivos de programa\Call of Duty Dawnville Demo/main
C:\Archivos de programa\Call of Duty Dawnville Demo\main\localized_english_pak0.pk3 (790 files)
    localized assets pak file for english

File Handles:
----------------------
3998 files in pk3 files
execing default.cfg
couldn't exec language.cfg
couldn't exec config.cfg
execing autoexec.cfg
Unknown command "cg_fov"
========= autoconfigure
configure.csv: using configuration 1200 cpu MHz 512 sys MB 32 vid MB
Hunk_Clear: reset the hunk ok
logfile opened on Sat Jan 03 02:43:52 2004

...detecting CPU, found AMD w/ 3DNow!
Measured CPU speed is 1.64 GHz
System memory is 512 MB (capped at 1 GB)
Video card memory is 16 MB
Streaming SIMD Extensions (SSE) supported

----- Client Initialization -----
----- Initializing Renderer ----
-------------------------------
----- Client Initialization Complete -----
----- R_Init -----
Initializing OpenGL subsystem
...initializing QGL
...calling LoadLibrary( 'C:\WINDOWS\SYSTEM\opengl32.dll' ): succeeded
...setting mode 3: 640 480 FS
...using colorsbits of 16
...calling CDS: ok
...registered window class
...created window@0,0 (640x480)
Initializing OpenGL driver
...getting DC: succeeded
...GLW_ChoosePFD( 16, 16, 0 )
...5 PFDs found
...hardware acceleration found
...PIXELFORMAT 2 selected
...creating GL context: succeeded
...making context current: succeeded
Initializing OpenGL extensions

GL_VENDOR: Brian Paul
GL_RENDERER: Mesa Glide v0.51 Voodoo3 (tm) 1MB FB, 12MB TM, 2 TMU, NOSLI
GL_VERSION: 1.2 Mesa 5.1
GL_EXTENSIONS: GL_ARB_multitexture GL_ARB_point_parameters GL_ARB_texture_compression GL_ARB_texture_env_add GL_ARB_texture_mirrored_repeat GL_ARB_transpose_matrix GL_ARB_window_pos GL_EXT_abgr GL_EXT_bgra GL_EXT_blend_func_separate GL_EXT_clip_volume_hint GL_EXT_compiled_vertex_array GL_EXT_copy_texture GL_EXT_draw_range_elements GL_EXT_packed_pixels GL_EXT_paletted_texture GL_EXT_point_parameters GL_EXT_polygon_offset GL_EXT_rescale_normal GL_EXT_secondary_color GL_EXT_separate_specular_color GL_EXT_shared_texture_palette GL_EXT_subtexture GL_EXT_texture GL_EXT_texture3D GL_EXT_texture_edge_clamp GL_EXT_texture_env_add GL_EXT_texture_lod_bias GL_EXT_texture_object GL_EXT_vertex_array GL_APPLE_packed_pixels GL_IBM_rasterpos_clip GL_IBM_texture_mirrored_repeat GL_INGR_blend_func_separate GL_MESA_window_pos GL_NV_light_max_exponent GL_NV_texgen_reflection GL_SGIS_texture_edge_clamp GL_SGIS_texture_lod WGL_3DFX_gamma_control WGL_EXT_swap_control WGL_EXT_extensions_string WGL_ARB_extensions_string
----- CL_Shutdown -----
RE_Shutdown( 1 )
Shutting down OpenGL subsystem
...wglMakeCurrent( NULL, NULL ): success
...deleting GL context: success
...releasing DC: success
...destroying window
...resetting display
...shutting down QGL
...unloading OpenGL DLL
-----------------------
Hunk_Clear: reset the hunk ok
Your video card appears to be missing one or more features required to run Call of Duty.

You should install the latest drivers for your video card, being sure to uninstall the old drivers first.  If you already have the latest drivers, you should completely uninstall the drivers and then reinstall them.  This fixes most problems.  If the game still doesn't work, it may be that your video card does not have the minimum features required.  Please check the readme for more information, including a list of supported video cards.

In 32bit I got the same message in the demo so possibly if I get the game, I´ll get it running

From the read me with full version.
""""""""
3. 16-bit color
 Call of duty does not support 16 bit color depth and does not provide this option in the menu system. Forcing  the game to run in 16-bit color through other mean may result in graphic corruption and other issues.

4. 16 bit textures
  Call of duty is optimized for 32 bit (high resolution) color textures. Since most of the textures and art in the game contain a 32 bit color palette, playing the game using the 16 bit texture quality selection only displays half the color information, thus causing some loss in visual quality.
"""
Sounds like it can run in 16 texture mode

hehehe...that's again the color depth problem, isn't it?
since cod only supports 32bit color depth and the voodoo3 only supports 16bit color depth (in 3d apis) you'll get this error message.
we tried to handle that problem but we had no luck, 'cause there aren't even 16bit textures delivered with the game...dunno about the other forums but i don't think anybody had luck to run your combination up to now, sorry