Launching the game with default wine settings do not work properly. The game window is very small and stays in the top left. This is caused by wine not properly loading the right patch DLL that is provided with the GOG install.

Here is how to properly install the game on Linux:

Step 1: Install the game with wine.
wine setup.exe

Step 2: Run winecfg.
winecfg

Step 3: Add an application and point it towards D3DPopTB.exe. Repeat this step for D3DPopTBUW.exe.

Step 4: Go to Libraries.

Step 5: Type in ddraw in the box and press add.

Step 6: Edit the Override to Native (Windows).

Step 7: Repeat the step for the other .exe.

Step 8: Now you can launch D3DPopTB.exe or D3DPopTBUW.exe using wine.
wine D3DPopTB.exe


Notes:
Launching D3DPopTB.exe will launch the original game while D3DPopTBUW.exe will launch the expansion.