To have the drag and drop feature to SharePoint Server 2013, here are the scenario or requirements of Web browsers.
- Internet Explorer 10
- Internet Explorer 9 with Office 2013 Installed
- Internet Explorer 8 with Office 2013 Installed
- FireFox latest version
- Chrome latest version
Hence, for IE 8 and IE 9, it must have Office 2013 installed on the machines, else the drag and drop feature will not be available.