Ok, after much effort, I finally got this to work. Here's how:
sudo apt-get -f install
sudo dpkg --add-architecture i386
sudo apt-get install libxt6:i386 libnspr4-0d:i386 libgtk2.0-0:i386 libstdc++6:i386 libnss3-1d:i386 libxml2:i386 libxslt1.1:i386 libcanberra-gtk-module:i386 gtk2-engines-murrine:i386
Note: the above command is similar to other tutorials, but without lib32nss-mdns:i386
as it couldn't be found. This was a huge PIA and a lot of googling to find the answer, so the replacement can be installed with:
sudo apt-get install libnss-sss:i386
Then, as with other tutorials, create the symbolic links with:
sudo ln -s /usr/lib/x86_64-linux-gnu/libgnome-keyring.so.0 /usr/lib/libgnome-keyring.so.0
and
sudo ln -s /usr/lib/x86_64-linux-gnu/libgnome-keyring.so.0.2.0 /usr/lib/libgnome-keyring.so.0.2.0
Then finally, make the Adobe installer executable with:
sudo chmod a+x AdobeAIRInstaller.bin
Then install it:
sudo ./AdobeAIRInstaller.bin
Now, it takes some time for the dialog to show after the above command, so give it a while. But when finished, you should see Adobe Air in your applications.
Then for completeness, delete the symbolic links with
sudo rm /usr/lib/libgnome-keyring.so.0
and
sudo rm /usr/lib/libgnome-keyring.so.0.2.0
So after all that, I tried to install Scratch 2.0 Offline (which was the whole point of the exercise) and it didn't work! Then I changed the permissions of the .air file to full read write execute for both current user and sudo and voila, it worked!