EULAs and stuff have not had extensive testing in the courts. We really don't know how far they can go. One day the courts might say "yeah, everything written in an EULA is perfectly enforceable" or they might say "it's enforceable but only to a point."
As for patches to existing games, that's a toughie. I can't find any cases (during my 5 minutes worth of searching just now) that address this. But there are cases that might have some relevance.
The motion picture industry sued Sony years back because of VHS and Betamax. Their argument was that Sony's manufacturing of recording devices allowed the end user to infringe on their copyrights by taping the programs. The court concluded that it was fine to sell VCRs because they serve substantial non-infringing purposes. What that means is Sony can sell a product that can be used for copyright infringement so long as that's not the only or primary purpose.
I'm not sure if that covers software but if it does then you would ask whether or not a software patch serves non-infringing purposes. I'm not sure it does.
But there's a theory called "market failure" that helped lead to the Sony decision. In the Sony case you’d want to allow fair use because the individuals using the VCRs are unlikely to be in a position to negotiate for a license with the television networks. The courts aren't blind to real world logic and good public policy like this. It's why thumbnails of images are not copyright violations even though they technically fit the definition. So perhaps it's good public policy to allow some software patches?
There's also a case called "Sony v. Connectix." In this case, the court said that making copies of a computer program for the purpose of reverse engineering might be permissible. So perhaps a patch could eke by by stretching this, especially since the patch itself technically doesn't use anything from the original (which is always a helpful fact for the defendant in a copyright claim).
Fair Use would be a good place to start.
There's a four part test to determine whether something falls under Fair Use:
1. The purpose and character of the use, including whether such use is of commercial nature or is for nonprofit educational purposes;
2. The nature of the copyrighted work;
3. Amount and substantiality of the portion used in relation to the copyrighted work as a whole; and
4. The effect of the use upon the potential market for or value of the copyrighted work.
The third prong is highly in favor of the patch creator since nothing of the original (at least I would imagine none) is actually being used. Of course using the patch in any way requires the entirety of the CT rom...so...yeah. But the fourth prong is really what's at stake here since it could really screw up SquareEnix's financial interest in Chrono Trigger. For example, if somebody releases a patch that turns a $20 piece of software into a free piece of software, that's going to really hurt the copyright holder. This patch isn't quite doing that but it could hurt the financial viability of the CT brand.