This is just becoming a silly definition war. I'm not going to even bother to define "PC", I think it's a meaningless marketing term these days for things that vaguely resemble the linage of the original IBM PC.
Obviously you don't, or you wouldn't be so up in arms about calling a console a PC. You seem wed to the term, I'm not - I'm using the proper term to describe the device as everyone has since the Atari VCR hit the streets.
But, I do think it is possible for all the things you listed to be "general purpose computers".
It's possible for a car to be a motorobike if you mod it enough. Saying you should call it that because it has potential to be one is a sign that you're gravely confused what words mean and their purpose in allowing coherent communication.
Now going back to the SteamBox, it is in fact both a video game console and a general purpose computer.
Which is exactly what I said. It's trying to be something in the middle, that's it's entire reason for existing.