Well, this is certainly a problem.
It appears in Font Book, in Library/Fonts, and in Library/Microsoft/Fonts.
That's an automatic font conflict. You can fix it by disabling one or the other in Font Book, but it's better to not have the ability to create a conflict at all and delete one or the other instance of the Century font from the drive.
No, Apple has not done anything to make it difficult to use one particular font. What could possibly be the purpose?
The main item here is the problem started when you upgraded to High Sierra. Bluntly, Font Bork is a terrible font manager. I can't tell you how many times, through multiple OS upgrades and updates that folks report fonts suddenly don't work right afterwards. At least 90% of the time, it's because Font Book's database gets hosed in the process.
Shut all apps down. Delete one of the same-named Century fonts. Restart the Mac and hold down the Shift key to enter Safe Mode. Login to your account when the password screen comes up. When it gets to the desktop, restart again normally.
This, among other cleanup procedures the OS does in a Safe Mode startup, clears all cache files from the user account you logged into in Safe Mode, and resets Font Book's database.
Try Word again.