As you might expect, Imagineer has used emulation to bring these titles to Switch, but it would appear that the company has failed to properly credit the author of one of the emulators used, the Game Boy Advance emulator mGBA. mGBA author endrift points to the fact that the title "contains strings matching settings names unique to [mGBA]" as evidence.
However, that's not the issue here – as the Video Game History Foundation's Frank Cifaldi states, mGBA's End User Licence Agreement allows for commercial use. The problem is that the credits for the emulator have been intentionally removed, which, according to endrift, means that Nintendo is "shipping a pirated emulator in a third party title".
How this has happened is anyone's guess, but the fact that mGBA's EULA allows for commercial usage makes the fact that Imagineer didn't approach endrift all the more baffling. The emulator's GitHub page even provides an email address for the commercial licensing of the emulator.
As for how this can be solved, it would be relatively easy for Imagineer to issue an update to the game which credits endrift for their work, but a worst-case scenario could see the game pulled from sale.
Endrift has stated that they have sent a message to both Nintendo of America and the Electronic Frontier Foundation, so a DMCA takedown isn't beyond the realms of possibility – although we'd argue it's perhaps unlikely to happen.
Emulators in themselves are not illegal in any way. In this specific case, mGBA is available free of charge to anyone under the MPL 2.0 license. This means anyone, including gaming companies, to simplify a bit, can use and distribute it, even for commercial purposes, as long as the authors are credited and the source and any modification to it are made available.
In this case, Imagineer has apparently distributed (and maybe modified) mGBA without making any mention of it, which is totally an infringement on endrift's copyright. She would be completely justified in requesting that Imagineer stops selling and distributing the games, changes them to respect the license, or failing that, sue them and ask for damages.
By distributing their collection this way, Imagineer is breaching endrift's copyright (this does not have anything to do with patents). Imagineer being a japanese company doesn't change much of anything in this respect, as Japan's copyright laws are very similar to most of the world's.
As for endrift reaching out to Nintendo of America rather than Nintendo of Japan or Imagineer themselves, I guess she might have tried reaching out to the latter two already, but aside from actually starting legal action, I doubt she'd get much attention from Imagineer unless she got the attention of another interlocutor such as NoA first, so that totally makes sense to me.