Rather, the issue would be straight-up copyright infringement: they’re hosting copyrighted ROMs and sending copies to any browser that visits the page. There are various little-known exemptions for copyright infringement, too, written in the statute, but I don’t think any of them are applicable. The Internet Archive would have to claim either copyright abandonment or fair use. Fair use would be a stretch, since they’re sending the entire ROMs, not just parts of them, and they’re offering a replica of the original, intended user experience rather than creating something “transformative”. As for copyright abandonment… I don’t know much about the case law for that, but at least according to Wikipedia[1], it wouldn’t hold much water either, any more than it would for out-of-print (but non-public-domain) books.
Heck, they’re even hosting games that are still being sold, such as Sonic the Hedgehog and Pac-Man. They’re marked “Stream Only”, but that just means they’re not putting a “save a copy” button in the UI; the game is still being downloaded in full into your browser, in order to run the JavaScript-based emulator. (Though even if they were running the emulator on a server and streaming a video feed, that would still typically be infringing.)
My guess is, they know they’re violating copyright, but they expect that the vast majority of copyright owners won’t care (and/or won’t notice), and anyone who does will send a DMCA notice rather than going for a full-blown lawsuit. Alternately, they might have negotiated a license for at least some of the games in the collection, but in that case I’d expect they’d say so.
https://archive.org/details/consolelivingroom