wouldn't the ARM SoC needed to emulate the NES be really, really, really basic?
I mean there is even a more or less OK emulator of the NES even on the PS1, without any official involvement
This needs to be better than just okay, graphical/audio glitches or extra slowdowns (perhaps even lack of slowdowns and flickering) aren't really acceptable.
PS1 has a really low end CPU by today's standards, a simple ARM microcontroller can easily exceed it. But imbnes was possible due to rendering the graphics with the GPU and sound with the SPU, and you'll probably have a hard time finding a microcontroller with suitable hardware or even much of a display controller. You could do it with a very low end SoC, like an Allwinner A13 or similar that costs < $5. But at this point you'll probably need external RAM and a PMIC (maybe you can find some SoCs that don't need the latter). It's not a huge deal, it's just the difference between saving a few dollars in chips.
It may actually be possible to do this with a higher end microcontroller, managing all of the emulation and video signal generation in software. Especially if you use a dual core one. It's hard to really say for sure, and I don't know if the pricing still makes that attractive.
another idea, couldn't they use something based on some of their portables hardware?
GBA or DS, while they can manage decent NES emulation, don't output the full resolution. So it's not really good enough for this. They'd have to go with 3DS. But I think if they used any of these chips as-is they'd need something to manage the HDMI output.
something else, isn't the typical single chip Nes clone solution made for composite video, and this thing is HDMI only or is it really simple to make it HDMI?
If there aren't any available with HDMI then that probably wouldn't really make sense anymore. I don't really know what's available these days. There are other requirements like the Wii controller compatibility that also make me think a third party NOAC wouldn't have really been sufficient.
I'm also now reading it supports save states, so that's most likely done with software emulation. Although I don't know how you're supposed to manage those with the controller. Maybe it just auto-saves when you power off and gives you an option to resume when you reload.