No, I never really run games from the Launch button in the installer itself. I did run the installer as administrator, but I'd already tried that previously and it made no difference, so no idea what made it work this time. The GOG shortcuts in the Start menu and such tend to force running as administrator anyway, so I'm pretty sure the game was always being run as administrator.

Regardless, it looks like some strange oddity at play, and I replied back to GOG letting them know that it worked, even though I'd not actually done anything any different.