Hi,
Based on the error message, this might be occurred that there is a problem with the Microsoft Software Protection Platform that is part of Microsoft Windows. Please read this KB:
https://support.microsoft.com/en-us/kb/2853971
Then, we can try some methods that worked for some customers.
1) Ran Word 2013 as administrator
Reference:
http://answers.microsoft.com/en-us/office/forum/office_2013_release-office_install/cant-activate-office-2013/b0b013cf-3883-40f2-99de-0706e34b0a79
2) Computer Name since the installation showed as activated in the Office 365 Admin with the Computer Name, yet was not activated on the actual computer.
Deactivate the computer's install in Office 365 admin screen w/o uninstalling Office=>Change the Computer Name in Settings/System/About=>Reboot
Reference:
https://community.office365.com/en-us/f/1004/t/402107
Hope it's helpful.
Regards,
George Zhao
TechNet Community Support