That's Linux Mint...
The Windows version won't work with Mint. At least not without a little workaround.
I've found the best and easiest way to use Digital Editions with Mint (or any other Ubuntu spin) is to install Digital Editions 2.0 via WineTricks. Which you can probably get from the Mint software centre.
When you open WineTricks you'll see a menu asking "what do you want to do?" You need to select the 'install an app' option. In the next screen select Adobe Digital Editions - 2011. Then just install as before; which is easier if you have your Adobe ID to hand.
The next bit I'm a little hazy about. As far as I recall I left Digital Editions open and downloaded an e-book (with Adobe DRM) via Firefox. In the download dialogue box I selected "Download with Digital Editions" and checked the "Do this automatically..." option. I'm not sure that Firefox will present Digital Editions as an option without Digital Editions being open. Though I could be wrong about that - it's 3 years since I installed the software.
Though you can read the e-book on your PC screen with Digital Editions, the better option is to use Calibre. Which you can also get from the software centre. Calibre has its own e-book viewer and will recognise and transfer e-books to most e-readers. You get this started by using the big + button in Calibre to import the e-book from your My Digital Editions folder to your Calibre library. After connecting your e-reader to your PC by USB you use the 'Send to device' button to paste it in to your e-reader.
Hope this helps.