Ok, I didn't let go and approached it again, and... I think I did it :)
Here is how it worked for me:
- Installed ADK as per link provided by Matthew Read.
- Installed the database server from the installation options.
- Ran Compatibility Administrator (32-bit) (In Admin mode)
- In the column on the left, on the bottom selected New Database.
- The top bar - selected 'Fix'
- Got a window named 'Create new ApplicationFix'
- Used mu own names in the first 2 fields, in the third one pointed to the location of Launcher.exe, pressed 'Next'
- Did nothing in the 'Compatibility Modes' window, pressed 'Next'
- In 'Compatibility Fixes' window scrolled down and ticked 'Force Admin Access'
- Pressed 'Test Run' - Launcher ran without asking for admin password (yes!), pressed 'Next'
- In 'Matching Information' window only left 'File Description', 'Company Name'and 'Product Name' ticked, pressed 'Finish'
I am not sure if the following 2 steps were necessary (especially 1), but I performed them...
- Top bar - pressed Save and saved the database in the same folder as Launcher.exe
- Top menu, from 'File' pull-down selected 'Install'
I only did all this like 20 minutes ago, but managed to run the game twice in the meantime, so hope this works for others as well