Any console is a "tiny PC." A tablet is a "tiny PC." Your smartphone is a "tiny PC." All these devices are more powerful than any PC from 10 years ago, for a fraction of the size. A PC doesn't have to be x86 or running Windows. A MacBook is a personal computer regardless of what Apple wants you to believe.
Also, this won't cost $1000. Mass-scale economies and costs absorption by Valve (who's freaking rich) will drive the price down. Should I remind people that for years Microsoft was losing money for each console they sold? They make money on the license fees for the games, not on the hardware.
The problem I foresee is the cooling. You can't have a powerful GPU if you can't cool it properly. If you want to cool it properly you need active cooling (fans, for instance). But this makes noise, and you don't want noise in your living room. The form factor will also be a problem for the cooling: you need smaller fans, which need to spin faster than large ones for the same amount of air flow. Smaller fans spinning fast are much noisier than their opposite.
This means the device will be either noisy, or not as powerful as it could be. Which is not necessarily a problem, since it'll have to run at 1080p max (maximum resolution for TV sets until 4K really takes off) - while on a PC the resolution can be 30-50% or more higher. Also you are father from the screen in your living room than when in front of your PC, so details matter less.
I'm very excited by this nevertheless. I only hope I can use my regular Steam library on it, so I can choose to play games on my PC or on my "Piston" console.