But if it's ROM-hosting you're talking about, then it will be harder for people to find specific games that are out of print, with no other way to legally obtain them.
They could probably point at virtual console at this point.
Anyway as for RHDN then probably not. RHDN purposely does not host ROMs, hosts patches which are basically useless by themselves (without the technical skills of a ROM hacker an IPS file is likely random junk), would be hard to demonstrate even the notion of losses from, probably does not have anything for a currently active online game and said patches typically should not contain any directly copyrighted material of the original game owner (or another IP owner, give or take spoofs but... yeah).
While they could possibly try something with derived works (or the local equivalent thereof), possibly whatever they went after subtitle sites with (though again such files are not useful in an of themselves, where subs are effectively a timed script readable by a text editor or simple program), or some kind of DRM circumvention (I once saw a game genie master code discussed) it would be a proper court case they have to fight if RHDN did stand up (the EFF I imagine would be interested) and not just buckle immediately. The results of said court case might also come out not in their favour and most companies will try to avoid setting a precedent that comes back to bite them. This also says nothing of the PR backlash that would likely result*.
Copyright infringement, or indeed outright knowing distribution by a commercial site, which is what ROM sites go in for (give or take the commercial bit at times), is far easier to sell to a court and does not attract a backlash.
*I am not sure the extent of it would be. I am sure we all saw the backlash for the Nintendo vs let's play set, itself something of a storm in a teacup and petered out fairly quickly.
Flash carts, emulators and mod chips are already considered a bit niche (and possibly a bit naughty thanks to years of propaganda) and ROM hacking is a niche within that niche for the most part**. I imagine it then be the people that knew about it would be far more bitter about it but so few in number that it does not matter.
**someone out there may well have got a game, wondered if it could be translated and came directly here, maybe were used to doing it for say a C64 where such things were the order of the day, or dreamt up the abstract concept from what they knew of programming in general. Fairly safe to say most here were already versed in emulators, flash carts, mod chips, the general "piracy" aspect of games culture and whatever else.