Nintendo's NES/SNES emulators have always been their own in-house tools. The NES/SNES Classic consoles did run on Linux, and Nintendo published the operating system source code as required by the software licenses, appropriately. The emulators are not part of the source release, and very likely derived from the same ones used on Wii virtual console (possibly older, Animal Crossing had a NES emulator on the GameCube too).
There's a popular myth floating around that Nintendo downloaded Super Mario Bros. off the internet only to sell it back to players via the Wii virtual console, but I'm only comfortable with calling it a myth because it's based on the fact that the embedded iNES file in the VC release is identical to iNES files you can find online. There's only one standalone version of Super Mario Bros. on the NES, and you can trivially recreate an exact file on your very own if you have the cartridge and a ROM dumping utility. It's a pretty good possibility that Nintendo created their virtual ROM in exactly the same fashion. The iNES format itself is very simple, and Nintendo hired the iNES developer to work on their in-house software; he could have easily just brought that same format into their official projects. (EDIT: This last sentence appears to have been another myth I bought into, see the reply to this comment.)
My understanding is that The "Nintendo hired the iNES Developer" story is actually it's own myth!
The person referenced who Nintendo hired is Kawase Tomohiro.
The basis for calling him "The iNES Developer" is that, in a changelog for 0.7 of iNES, Marat Fayzullin - the developer of iNES - wrote: "Sound support completely rewritten, thanks to Kawase Tomohiro"
That is the entirety of the association. That single line in a changelog. Based on similar "thanks" lines it was probably because they reported some emulation issues and not because they personally rewrote the sound support for the emulator, but resulted in Marat doing so. It's actually interesting how these stories seem to change over time. The last time I heard this, the story was that Nintendo had hired somebody who contributed to iNES, which was at least technically true if a bit misleading, but it seems that now the story is that they hired *the* iNES Developer. Which seems particularly silly when we consider the basis is that 8 word changelog line.
Could be buying into the myth, but I read somewhere that there was header or metadata in one of the ROMs that basically betrayed that it had been downloaded from a popular ROM site. Is that not right?
