Games

please get a personality

Well yeah, as the owners they have the exclusive right to determine what's okay. They're just following the rules as they've been laid out by centuries of corporate lobbying for more exploitable copyright laws. Those are what we need to focus on if we want more fair use of intellectual property that the rights holder has already sufficiently profited from - the thing that such protections were initially meant to ensure to a much more reasonable extent.

I believe they do have their own emulator. It logically would be what powers the Nintendo arcade

In other words, emulators are crucial for game preservation? This shows that Nintendo knows that, and when they say it's not the case, they're not simply wrong, they're lying.

Any other museum wouldn't be a hypocrite for doing so.

This is a "Museum" run by Nintendo in Japan. Meaning they could have used or even created more original hardware to run the titles, but instead cut costs by using the same Emulators that they're hoping to take down.

That is highly depending on the type of Museum. Many Videogame and Computer Museums (at least in Germany) are showing the real Hardware running, some are even allowing the visitors to use and play at the old machines. And yes, they are often very used to repairing the hardware too.

I would expect from Nintendo that they would show and use real hardware in their museum, and not some emulators. Because I can see the games on an emulator at home (for example using my Switch Online or my SNES Classic), I don't need a museum for that experience.