So even though Apple uses x86 processors and technically it is a personal computer, "PC" still refers to the old brand name that is synonymous with Wintel. Apple has personal computers, Microsoft has Personal Computers.
Of course it is, and much of what is sold with that moniker today is really more of an entertainment appliance than "computer." When my daughter was 5 or 6 and being told to "dial 9-1-1 for emergencies" she asked me "Why do they call it dialing?"
So the interesting thing from the perspective of the Steam box is this is an entertainment console with a bunch of details about how the insides work. I'm sure that 95% of the people who buy it will have the exact same experience they would have had if they bought and Xbox One or PS4, and the other 5% will have a lot of fun making it do amazing things and not have to worry about getting sued or arrested for it [1].
[1] http://en.wikipedia.org/wiki/Sony_Computer_Entertainment_Ame...
When the term PC was coined, computers were fridge sized horrifically expensive things that ran in research institutions and very large companies. The idea of having your own was...crazy.
It is weird how the name has come to mean something based on the Wintel nexus, but that's marketing and differentiation for you.
Those sound an awful lot like PCs to me. Sure, they have a bit of custom hardware design, but for the most part are basically just PCs; except that they're locked down and you can't write your own software for them without going through an intermediary (and if you try to, you may get sued or arrested for hacking).
I see the Ouya mainly being appealing to gamers who are mostly interested in casual and retro titles, which it is no doubt more than capable of handling. The point is that they are not trying to be a traditional powerful console, they are trying to be what a large group of people (who have traditionally been interested but not interested enough to shell out for a traditional console and its expensive games) are wanting. The fact it also doubles up as a media centre machine, aims to work out of the box (the cheap devices imported from out east are sold as basic Android units with little care for polishing the software install so the user needs a little technical knowlege to get things like XMBC and its ilk to work), and is fairly cheap, makes it quite an attractive package unless you need/want more power (in which case there are better solutions for you out there already).
EDIT: I've just checked and the Ouya runs off the Tegra3 and has 1Gb RAM, so it has oumpf than I thought when writing the above. That is essentially the same chipset choice made for the G1 Nexus 7 so noticeably more powerful than any cheap tablets and phones. It won't match the high power shiny now consoles and play their graphically demanding titles of course, but again I don't think that is the aim and it should be be able to deal with some relatively demanding games (and they'll be very inexpensive compared to the AAA console/PC titles).
Browse the file system? Very easy. There are many free and paid file managers. You can also use a terminal emulator.
Obtain root access? OEM unlock bootloader, throw su on the phone and you are set.
Recompile and update the kernel? I has never built my own kernel, but there are many custom kernels popping up all the time.
Replace the window manager? To change the desktop environment, most people just install a different "launcher". That changes how the desktop, windowing, and general interface operate. If you really wanted to have the full freedom of Linux, you can install something like Debian on an android device with a dual boot setup or run it on top of android through a VNC client.
I would prefer a fully free software stack, but I realize that that's not always possible, so I like to support the next best thing. Traditional consoles have always been so hacking unfriendly that I have refused to buy them.
Just so you know, a Nexus One was the first cell phone I ever bought; it was the first that I considered free enough (and capable enough; the Dream/G1 was just a little too clunky for me to consider it particularly useful).