This is done through Office Online, which does not require a desktop version of Office.
From Dropbox’ end, users can now open files straight into Office by clicking the “Open” button.
Meanwhile, in Office, users will be able to navigate through their Dropbox account and find the desired file to edit. In both cases, editing can be done directly in the browser and changes will be saved back into Dropbox.
The integration is part of an ongoing partnership first announced in November, and comes in light of other integrations on iOS and Android.