IE may be interfering here as well - I've found IE often tries to be 'helpful' and open documents within the browser, happens similarly with powerpoint for us, and we have had no end of issues where stakeholders want *this* powerpoint to open in office but *this* one to open in presentation mode, etc, etc. So you get to a situation where the individual desktop can be set up so opening the same file locally does one thing and the exact same file opened from a link does something else. Non-microsoft browsers seem to simply download the file (and again stakeholders wanting us to write web code to control this behaviour as well).
Possibly nothing to do with it, but we also had an issue where Apache didn't have the new MIME types, but Matrix did. So while in under construction / safe edit downloaded fine, mime type correct, but once published (and served by apache) was downloading as a zip file.
Double-check your response headers, MIME types should be:
.docx application/vnd.openxmlformats-officedocument.wordprocessingml.document
.dotx application/vnd.openxmlformats-officedocument.wordprocessingml.template