First of all on GoG release you need to proceed to game folder and rename "_Movie" folder to "Movie" without underscore. I am not sure about other releases of the game, they might not need this step.

Now, forcing the game to play music and video files requires emulation through DXWnd - the emulator for old games which you can find at sourceforge:
sourceforge.net/projects/dxwnd/files/Latest%20build/

Download the latest archive, unpack it wherever you want and start dxwnd.exe
Be advised: the archive is a "rar"-format, you will need software like 7zip to unpack it, grab it here:
7-zip.org

Now you have two options:

• Option 1.
You can download my configuration file for Pax Imperia from one of these links:
mega.nz/file/xTZQhBYI#s3qUsIP47FtWNzqrVP8P_TLxUnvA8kAHp3JDWOZnsds
drive.google.com/file/d/1utNFsCE1m_STDaULvbpT3JlbWyAQkH9V/view?usp=sharing
www.dropbox.com/s/p4i60j22jfn1xvq/Pax%20Imperia%20Eminent%20Domain.dxw?dl=0
cloud.disroot.org/s/bdM9FEs9LPGsQcX

Next in the emulator window go to top menus and click "File" - "Import" then choose the configuration file you have just downloaded. Now emulator window will have a new icon - that is a shortcut to start the game through emulator. Right click on this icon and in the menu select "Modify" - it will open the settings window.
The very first tab has a "Path" setting, you need to change it to your installed game executable, click the button with three dots on the right and find "Pax Imperia.exe" on your PC, select it, click "Open" and after that click "OK" in the settings window.
Now all you have to do is to save changes. Proceed to top menu in emulator window and click "File" - "Save" and there will be a popup window asking if you are sure, click "Yes".

• Option 2.
If all the links to my configuration file are dead or if you aren't enjoying the idea of downloading random unknown files from random file hostings - then you can configure all the setting yourself.
That is why here is a screenshot with all the settings:
i.imgur.com/tQz6nYC.png
i.ibb.co/JssLsyK/Pax-Imperia-DXWnd-settings-for-Windows-10-in-2022.png

You need to start the emulator with dxwnd.exe and double click the game icon in emulator window to start the game.

Be advised: there is a small bug, any ingame video can freeze on the first frame and in this case you can revive it by simply left clicking anywhere to make it play or you can press spacebar to skip the video.

The game will run in fullscreen with a proper ratio of 4:3 and with working music and video.
Some people for some reason prefer to play it windowed, if you need your game to be in a window, change in the emulator settings:
"Main" tab - change "Desktop" to "Desktop center", this will make game run in a window;
"Main" tab - you can disable "Hide desktop background", this will stop hiding your desktop;
"Video" tab - you can change "modal" to "thick frame" if you need to have window borders;
"Video" tab - disable "Hide Taskbar" to reveal taskbar.
You can also try to play with mouse settings in "Mouse" tab in case you need to release mouse outside of game window, but it was causing bad game behavior in my experience.

Thanks for the comprehensive desription. I've tried both, setting up the config manually and importing. Unfortunately I encountered problems with both solutions.

Using the imported file works well despite that the music is running loudly and can not be tuned down. The manual configuration repeatedly resulted in crashes but not always. Mostly during the play of the videos.

To change volume you need to enable *Expert mode*.
Then you need to open imported profile.
1 On tab 'Souind':
1.1. enable 'Emulate volume'
1.2. set CD Volume to some value (I set around 20%)
2. On tab 'CDAudio'
2.1. Enable 'Emulate CD mixer'
2.2. Set 'emulated CD volume'
3. On tab 'Compat'
3.1. Enable 'Hook GOG libs'

For me videos are getting stuck with codec, provided by GOG.
I managed to get it to work by using last 3.1 smack codec from here github.com/vogonsorg/radgametools with 'Async Blit Mode' enabled on 'DirectX' tab of DxWnd profile.