I know how find the GNOME version via terminal.
But is there a command or some other way that opens a window like this?
Simply put, there is no such window any longer. Particularly with Ubuntu, and more over if you're using the Gnome3 PPA, the multiple components which make up Gnome are a number of different versions. Many of the applications like Files (aka Nautilus) have an 'About' under their menu, however their version may not match other components.
Just as an example, my Files shows version 3.8.1, whereas my Gnome contacts shows version 3.6.2. Long and short of it however is that gnome-shell itself has no gui representation of its current version.
gnome-panel --version
orgnome-about --gnome-version
for output in terminal. I am not sure about the window, sorry.apt-cache show gnome-shell | grep Version
does also work