Your forgetting the co-processor which was also a dedicated ARMv6 chip much like the pi's although I think it was at a much lower CPU clock, it was dedicated to interfacing with the GPU and sound processors, think it could also do some floating point work too although the 333MHz mips could also do that.
The main issue here will be a console bios and game media. Most older console have a small area of ROM which when you turn the console on tells the CPU how to go and get the game from the storage medium (lets say a gameboy cartridge). On consoles that appear to have a full OS its a little more complex but in the case of the PSP what it actually does is load its rom which then tells it to load the built in OS seperately, this OS then reads the disk, gets info about it and maybe plays some music/films etc instead, when you select to play a game the console reboots with a RAM value saved that this time tells the ROM to boot the UMD not the built in OS (the home button is yet another thread that the PSP always runs and again forces a console restart to return to the main screen).
On the pi I assume your writing your game to run on linux which will add an overhead the consoles don't have (of course current and next gen consoles get even more complex with new features like dashboards etc). With the pi being more powerful though it probably isn't a massive issue, hell quake works. But it does make the idea of distributing the game harder. YOur game on its own might fit easily in a 256mb SD card but you would need linux and supporting drivers for your controller etc aswell meaning you might need a full gb SD card instead. OK sd cards aren't a huge problem but then you have peripherals too. How are you going to standardise what controllers people use and take into account different models having their own quirks that will influence gameplay.
Using the pi as a gaming machine: Possible
Feasibility of actually marketing it to users (even as open source): Not so likely
Similar hardware to the pi could quite easily be packaged up into an actual piece of dedicated console hardware and sold commercially though if you had the backing and resources to do so.
An alternative to using SD cards would be to take the route used by the OUYA which would be to run a system like android on the console (OUYA is infact using android 4 with an alternate homescreen etc as its interface) with its own marketplace. You would make a custom linux distro (android again is a linux distro at the end of the day) which boots upto the console interface. This distro would include drivers for a gamepad of some sort (we'll take the xbox 360 wired controllers) and its interface would solely be controlled via this gamepad. It would then have its own market type app directing you to download games for the system , in order for games to be featured in this market you can simply demand that they are compatible with the gamepad of choice. Its doable but not needed when one can just simply install a game under linux anyway.