Hi Erin,
>> Do I need to have Microsoft Office installed on the server if I want to set it as Word?
Based on my knowledge, we need to install Office on the server to do this. Besides, when we use Group Policy Preferences, please pay attention to F5-F8 function keys.
Regarding this point, the following article can be referred to for more information.
Enable and Disable Settings in a Preference Item
https://technet.microsoft.com/en-us/library/cc754299.aspx
In addition, if we don't want to install Office on the server, we can try to configure the setting on a Windows 8/8.1 with both RSAT and Word installed or a member server 2012/R2 with GPMC and Word installed.
Best regards,
Frank Shen