This is all fun speculation, and I feel like its best that if you have some input (and reasonable evidence, of course... like sources or something) then tell all in the comments and contribute to what the Polynauts' idea is for what this next Steambox will be.
It is Linux-based
...No surprise here. If there's one thing Gabe hates more than Windows 8... I'd rather not know what it is.
Intel + Nvidia CPU/GPU Combo
In Gabe's most recent keynote, he mentions getting Nvidia to optimize their drivers for Linux computing. When mentioning his "Good/Better/Best" hardware scheme, the "Good" always involves Grid, a streaming mechanism for Nvidia-based graphics cards (watch Borderlands 2 being streamed to an Ouya here). Combine that with his praise of recent Intel CPUs, and I think this will be a console AMD has no business in (and thank goodness because the drivers issues in my 7770 drive me mad). As for specifics, I couldn't say which processor Valve may use (Haswell is most recent, but Sandy Bridge is best for overclocking).
What about Windows Games?
So the obvious Achilles' heel of running a Linux-based gaming PC is how to deal with competing against and an operating system that has kept a strangle on PC gaming for just about 2 or 3 evers. Time has proven that there are almost no major publishers willing to port games over to an unproven operating system, even onto a proven platform. Valve knows this, and its clear they don't want to start from scratch. Yes, Every Valve game on Steam is available on Linux, but Gabe said last year that "We want to make it as easy as possible for the 2,500 games on Steam to run on Linux as well." That doesn't sound to me like begging publishers for Linux recognition; it sounds to me like Wine, a software program allowing Windows software to run on Linux. By no means am I saying this is a permanent solution to the problem, nor am I saying this indicates Battlefield 4 is going to be flawless here, but it does help a lot with older game legacy. Could Valve be working with Wine to optimize it for their platforms specs? Plausible. That said, Gabe has mentioned that Windows will be available for installation on the Steambox (see the first link), so there's a more robust (read: expensive) solution for you. You just stream them.
I am expecting Valve to finish the Big Picture Mode interface. The interface as it stands cannot access local media outside of games, or do much besides a web browser and a game launcher. What they've implemented this far is excellent, but not enough. I don't think this full BPM will be exclusive to the steambox.
Will We See a New Game?
Honestly, I think we will. The only rumors I've seen point towards a third Left 4 Dead, possibly running on Source Engine 2.0. Ok maybe not