TECK HAVEN: July 2024

Note: All tools used are linked at the bottom of the post.

Locate the Maps .ibd file that contains the textures you're looking for. For the Steam version of the game, they can be found in this directory:

Steam\SteamLibrary\steamapps\common\Deus Ex Invisible War\content\DX2\Maps

Note: If you're not sure which .ibd file has the specific texture you're looking for, the method I used was downloading any texture pack mod, such as the Deus Ex: Invisible War ESRGAN Pack. You don't need to install anything or add the mod to your game, you can simply view the contents of the files in your file browser. I used this to scroll through all the textures and visually find the file I wanted, and thus the name of the file I was looking for. I searched for this file in the Deus Ex 2 Materials Spreadsheet (created by Akven on ModDB) to determine the original texture database that particular texture was from (found in the MLB file column on the right).
After locating the .ibd file, you can copy it and paste it in another folder on the desktop, and use that as your working directory.
Next, download the Thief 3 Tools .zip from Thief 3 Sneaky Upgrade on ModDB. This .zip file contains the tools needed to extract the textures from the .idb files. The particular file we need from that .zip is ibt_xbt_ibd_texture_extract.exe. Unzip the archive and drag this .exe file into the folder you created earlier with the .idb file you want to extract.
Double-click the .exe file, and it should run automatically on the .idb file in the folder, producing a subfolder called "Extracted" in the same directory.

Note: I was describing how to find a specific texture in this guide as I didn't want to extract everything, however you can just extract all the textures by placing ibt_xbt_ibd_texture_extract.exe in the Maps folder and running it there instead, and all the textures should extract into a new subfolder called "Extracted" as before, but within the Maps folder.
In the Extracted folder, all the image textures found in the .ibd file should be extracted in .dds file format.

Note: If you want to edit the files they can be opened in an image editor, such as Photoshop, however a .dds file plug-in may be required, such as NVIDIA's Texture Tools Exporter (or the legacy version if you don't have access to a CUDA-accelerated GPU) or Intel's Texture Works Plugin. Links are provided below.