It was not yet announced if PS4 and Xbox 720 are going to have any backward compatibility. Both of them change their architectures to x86, so it's not that unlikely that they would not have any (especially PS4). And if they would it would be some kind of emulation -- the thing Valve also can do using Wine. Yes, it would be hard to get EA, Activision, etc., on their board, but it's hardly a Linux-related problem.
Sony has an alternate solution from buying Gaikai for people to stream games. It isn't the best solution due to latency and requiring good internet speeds, but it is an option. I see Microsoft having to do something as I don't see people just trashing all the 360 purchases they made over the last several years, especially ones on xbox live. Yes both cut out BC eventually, Nintendo did too, but it was there at the start to try and help bring along customers. With WINE they could get games working, but the time needed to test and verify everything would be huge. Valve only has about 300 employees from what I read. It would be on the developers/publishers themselves to get things working with Linux.
Valve is obviously dividing their own business to two different markets with this move. Then again, so did Microsoft, when they entered the console gaming business with XBox and didn't just continue publishing Age of Empires 4 and 5 and Midtown Madness 4 to PC machines.
If people have a gaming PC, and the Valve box won't run most of their steam games, they have no reason to get one. As stated earlier in the thread, just run an HDMI cable to your TV and be done with it. Valve will keep releasing everything on PC as they would lose too many sales not to.
If they aren't aiming at the PC gamer, then they are targeting primarily console gamers. However they tend to go where the 3rd parties are and where their friends play. Which is either with Sony or Microsoft. As is it it's looking like a niche product for people that like Valve/indies and don't want to buy or build a PC for gaming.