ESA's position, broadly, is:
* Game publishers own their titles and are entitled the economic benefits that stem from them.
* There is no exception in copyright law for "maintaining access to matchmaking services", and, more specifically, retaining access to online services isn't a use case that falls under fair use.
* The duration of copyright lasts far longer than "6 months after the matchmaking service stops working", which is the time threshold in EFF's exemption request.
* Game titles themselves have value separable from their online services, and indeed many/most games with online components charge separately (either directly or through agreements with the game console online services), further suggesting that the termination of online services doesn't impact the copyright on the game itself. Indeed, ESA contests the idea that these games are "abandoned" at all.
* The modifications required to substitute a new matchmaking service are intrusive and impact features other than those needed to restore matchmaking, creating a legal ambiguity.
* Similarly, the modifications extend far past the games themselves and into the consoles/phones/whatever, creating an ambiguity about whether/when jailbreaking limitations are contractually enforceable.
* Ambiguities aside, the technical capabilities that would need to be exempted to make this work are so sweeping as to potentially moot the copyright of most of the code on the platform (ie, to restore matchmaking, you'd need to exempt reversing and modifying and trafficking in the modified versions of entire closed operating systems).
* The beneficiaries of game modifications will include commercial entities who will gain legal cover for selling services that capture benefits that are rightfully owed to the game copyright holder.
... I'm about 1/3rd through their response and I've probably failed to capture 1/2 the ESA arguments I've read so far.
The sad thing about this is, even with ESA's arguments charitably summarized and faithfully captured, virtually none of EFF's audience is going to be persuaded. There was practically no risk that ESA would persuade EFF's audience. Should video games be legally hackable? Virtually everyone who cares what EFF thinks believes: "yes!!^$!".
There was absolutely no reason for EFF to be deceptive about this. And yet, here they are again, insulting our intelligence. EFF does a lot of good and important things, but their online advocacy is not one of them.