[JavaScript Error: "Could not remove C:\Users\[…]\AppData\Roaming\Microsoft\Word\STARTUP\Zotero.dotm" {file: "resource://zotero-winword-integration/installer.jsm" line: 186}]"

Zotero can't update the Word plugin. You (or, I would assume, your IT department) will need to either adjust your security software to let it do so or install the plugin manually. Note that you're likely to run into problems like this in the future if you install it manually, but it would work for now.