This is kinda easy once you know the right command. I had to un-install Adobe AIR from my Ubuntu system after the last point upgrade. I upgraded from the Update Manager and apparently, that broke Adobe AIR, because I could not use any AIR apps afterwards and AIR would not install again.
Open a terminal and add this line:
sudo dpkg -r adobeair-enu
You have to type in your root password and then wait for it to un-install. After it is gone, you can proceed with making your AdobeAIRInstaller.bin file executable; chmod +x AdobeAIRInstaller.bin and then start the installer; sudo ./AdobeAIRInstaller.bin.