You do not need to install the full Android Studio SDK. Your device should show a popup to authorize your computer to connect to it - accept this and then click the Refresh devices button again. Next, disable every debugging setting already activated and repeat the steps described before. First make sure you have installed Android Debug Bridge from Android Tools on your computer in order for it to be able to connect to your device.
If it still doesn’t appear, it may be because the link between your Android device and your computer is not authorized yet. If your device doesn’t appear in the lefthand side of the about:debugging page, try clicking the Refresh devices button.