Found the solution not on the web, so I'm posting this.

Issue: With a non-admin account you can play Tropico 5 only in English, even if it set to German via the provided language_setup.exe setup application. If you start the game while running an admin account, Game runs in German.

Specs: Tropico 1.10, latest GOG installer as of 23. 1. 2020 (released 1. 12. 2017), Win 10 64-Bit

Install Tropico 5 on Win 10 as a admin by using an admin account and clicking „Ok“ on UAC or by using the restricted user account and enterin the admin password at the UAC. Does not matter. Install it for all users on the machine. Select at language setup („language_setup.exe“) German as your prefered language.

Result: Start Tropico 5 from admin account and game starts in German. Start game from a user account and it starts in English.

Manually setting German in language setup has no effect. Even if you start the setup from a user account.

Solution:
1. Open „language.ini“ in Tropico 5 folder.

2. Look for your preferred language. It‘s something like this:
„[German]
RegPath=HKEY_CURRENT_USER/Software/Haemimont Games/Tropico 5
ValueName=Language
ValueType=String
Value=German“

3. Open Regedit

4. Add missing string in the format given by ini file.

Edit [Step 1]:

I mean "language_setup.ini", not "language.ini"