It wasn't easily obvious, nor did it come back to my memory until I was reminded by this website,
but after downloading a .bin file, you change the file to executable, and use ./programname in a terminal window to run it as an executable.(./AdobeAIRInstaller.bin)
It also appears that when I go to Tweetdeck, it would install Adobe Air anyway?
Nice to have Tweetdeck again.