As I said, I had tried "everything" and that includes the "add-architecture-i386" fix. I have the proprietary Nvidia driver installed.
pebcak yourself, I linked to a very long list of google results for this very problem, suggesting quite strongly that the problem does not just lie with me but with the way in which Valve choose to roll out the Steam client. Or are you suggesting that dpkg -i steam.deb and resolving some dependencies is beyond all of those Linux users? Or maybe the problem does actually lie with Valve.
Somehow I managed. 'dpkg add-architecture i386' ? Also, the steam client never asked for a driver on my machine. Proprietary nvidia does the magic I need for everything to run.
pebkac?