Ok, utorrent for Linux, is not the same as utorrent for Windows.
Its not a standalone gui application. it is a server, access by a web interface. A lot like the now defunct torrentflux.
Short answer is: What you have is a compressed archive that needs to be decompressed.
From the directory you download it:
$ tar -xvf utorrent-server-3.0-25053.tar.gz
$ cd utorrent-server-v3
$ ./utserver -daemon # to run it in the background, you can omit this and press ctrl + c to quit at any time
From there, you would want to open a browser window and point it to http://localhost:8080
to get to the web interface. Although, i get an "invalid request" when i get to that point.
If all you want to do is download torrents, I would recommend deluge, as being on par with utorrent, and has a similar feel to it. You should be able to install deluge from the package manager.