Thanks, I had not found that page.
For GalCiv itself, I tried successively:
* set compatibility mode for colors
* run setup as normal user
* run dart_setup as normal user
After that last step GalCiv started and seems to run fine.
AltarianProphecy also starts, but only displays a black screen and stops after a couple of seconds.
Setting compatibility mode for its exe too finishes the job.