To do this from within Word or other Windows programs, or by right-clicking a file in explorer and choosing Send to -> Mail recipient, you need a MAPI client to intercept such requests. One such client is tvhgooglemapi:
Tvhgooglemapi is a simple tool that pretends to be a real mail client to windows but really only uploads the mail to the drafts folder of gmail and then opens the draft in the default webbrowser. For the user this is almost exactly the same as having the gmail web interface as the default mailclient for some windows applications
You'll need to have Java installed for it to work, and IMAP enabled in your Gmail account.
By the way, when I first ran it, the window prompting for my Gmail login credentials (my Gmail address and my application-specific password) was hidden under other active windows, but a couple of alttab later, all was well.