As you've seen clicking a link just results in a normal download via GET, and then the downloaded file is opened and edited.
To open the file in an editor from its original location (using webdav) you need to use an extension to make a call to the editing program. On internet explorer you can use the sharepoint dll with ActiveX code:
Set EditDocumentButton = CreateObject("SharePoint.OpenDocuments.3")
strDocument = 'http://localhost:8080' + strDocument;
EditDocumentButton.EditDocument(strDocument)
Using Office Web Apps, Can you open a document via webdav?
I have heard that similar capabilities are available in Chrome and Firefox, but dont have details.