Of course, the game was written for xp, but then, there are some workarounds for running it under win7 (though you're right in the observation that under win8, there's no obvious chance of doing so).
To get an overview, see this page - seems a good one: pcgamingwiki.com/wiki/American_Conquest Then, if you're still looking for a solution, search for something like "american conquest - windows 7 compatibility" or "colour fix" (CDV-Forums?). The main thing for me was quite simple: Install the programme under win7. Press "Ctrl + shift + esc" to see the task-manager. Now kill (!) the "explorer"-service. You won't be able to navigate through windows the way you're used to. Instead, press the "execute"-button and look for the dmcr.exe in your game directory. Execute and have fun! To return to normal Windows, get back to the task-manager and simply execute "explorer" or "explorer.exe" Of course, you must check if there's need for the "compatibility mode" - see the previous posts!

Netestoval jsem.
Tady ovšem píšou něco o GOG verzi: https://pcgamingwiki.com/wiki/American_Conquest#Availability
Ta by měla fungovat všude. Tak si ji sežeň.