The application isn’t yet available in Google’s official repository so you won’t get automatic updates like you get with other Google products for Linux, like Google Chrome. So for now, you must check when a new version is released and manually download and install it.
Also, Google Web Designer doesn’t integrate with Unity’s global menu for now. Other than that, the application worked great in my test under Ubuntu 14.04.
Mac 10.7.x or later, Win 7 or later, Linux (Debian/Ubuntu/Fedora/openSUSE)