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.)