So you made this edit.
Now there's minor contradiction what you said and image you linked. Last time I checked using Dualshock 4 via bluetooth is next to impossible as controller automatically disconnects itself in couple minutes without any external programs or tools, even though it's detected and pairs fine as "wireless controller". Only way for me has been using it with regular USB cable but you clearly aren't using it.
Or did I perhaps miss something? If you are using only Dualshock 4 without any tools (software or hardware) Windows should show the controller up like in the top picture: http://imgur.com/a/eXrsD