ecokumm: Yep, this is an issue that's been plaguing the game ever since the sequel came out. As stated above, it has something to do with both versions of the engine not being able to play along together. Because of reasons.
BUT! There is hope! I actually found a solution that worked for me:
1) Run The Suffering. Play for a bit, then exit.
2) Run Ties That Bind. Play for a bit, then exit.
At this point, The Suffering should be having the missing textures issue
3) Run REGEDIT
4) Go to HKEY_LOCAL_MACHINE > SOFTWARE > Wow6432Node > Surreal > Riot Engine
5) Delete "SettingsDX105"
6) If you attempt to run The Suffering now you'll get an error, so you'll want to run suffering.exe with the -setup modifier
You'll have to configure the graphics in the launcher again as you did the first time, but both games should run OK now. God knows why. I just tried this in the GOG versions, I went back and forth between both games several times, and they're running without any issue.
I'm on Windows 10 Pro with all the latest patches.
Credit to cornoratu @ fileforums dot com
Thank you so much, this worked for me, god bless you.