Pretty sure the emulators there run locally, so it's of dubious legality.

They're a library. Their ability to serve binaries isn't dubious.

Last I checked you can download permanent copies of old roms on archive.org. I don't know how that's legal, I've always assumed it was just that nobody cared to DMCA any of it. I'm fine using it, but if you're being a huge stickler for legality I don't think it's clear.

They have a DMCA exemption: https://archive.org/about/dmca.php

Nothing in that article suggests hosting ROMS for download is legal. Said article states the original media is required for the exemption. Hosting ROMS does not require the Downloader have the original media.

Nor does archive.org have any special "exemption".

They have an exemption to the bypassing DRM rule on software, not one stopping DMCA takedowns.

Thanks for researching this.