Sublime Text 3: Drag & Drop, Move & Create a copy of files & folders

Obvious feature is not implemented, though I suggest you to use Sidebar Enhancements, a really great plugin to manage the sidebar stuff in ST2/3. (Jul. 24, 2017: Only ST3 as the repo notes)

Though it may seem obvious, but the sidebar is really poor in sublime text. There are requests on the official userecho page about that like this one.

I'm sure it will be implemented some time later. You also should not forget, that sublime is keyboard-oriented editor, as Vim was. That's something rare these days and is a feature. You may bind everything to keyboard or implement yourself using build systems and plugins.

delete the file(s) you wish to move then drag and drop from the recycling bin to the folder you wish to move them to. make sure it doesn't permanently delete your file before you do this.