If you don't see Zotero Word in the Extensions window at all, re-download and re-install Zotero.
If you see the folder icon and the export is not working, try this:
No, the Zotero desktop program and Connector work on your laptop or personally-owned computer, not on NPS-networked computers.
When on networked computer, you can add and edit items in your online zotero.org library in the cloud, but you cannot use it to cite in Word.