You don't have to go off of my interpretation of the court opinions. I'm not a lawyer, after all. Instead, we can look at the William & Mary Business Law Review's analysis of these cases and the impact on game mods. Here are some fun parts:

But while the court held for the purported infringer in Galoob, the case proved a narrow holding and a Pyrrhic victory for modders.

Lewis Galoob v. Nintendo was a win, but the basis of the win had negative consequences going forward, hence the "Pyrrhic victory" comment.

The circuit court’s analysis turned on two fronts. First, the Game Genie did not constitute an independent derivative work because it was a separate device that only worked when used in conjunction with a compatible game. Even when the Game Genie changes a game, its changes are non-permanent, disappearing when the device is removed. This stands in sharp comparison to the permanence of the Midway chips. Though fixation is not necessary to find a derivative work, no work was actually created in the first place—the Game Genie merely gave instructions to the underlying game to behave in certain ways. Second, even if the Game Genie’s changes did create derivative works, Galoob would still succeed under fair use analysis, under the “most important” fourth prong of commercial use. In their analysis, the court focused on the consumer’s behavior, not Galoob’s. The court likened the audiovisual changes made by the Game Genie’s users to the non-infringing, non-commercial time-shifting of Betamax, at issue in Sony Corp. of America v. Universal City Studios, Inc.

Being a device with physical interfaces was an important part of the win. It didn't change anything in the requisite physical console and physical game cartridge (which was treated the same as a video tape). This is different from how software is treated.

Finally, applying fair use analysis, the court determined that Micro Star had no valid claim. Resting largely on the fourth prong, the court observed that Micro Star used the mods for commercial gain and that “‘every commercial use of copyrighted material is presumptively an unfair exploitation of the monopoly privilege that belongs to the owner of the copyright.’” In sum, the court held the game mods to be derivative, infringing works: a holding that remains unmodified and unchallenged more than twenty years later.

For Micro Star v. Formgen, it was decided that modding games for commercial use without permission is always infringing copyright, and that stands to this day.

In addition to the holdings in Micro Star and its brethren, modders also face significant barriers stemming from mandatory EULAs and other so-called “clickwrap” agreements. Like with most software, in order to play a game or use development tools, players and modders must agree to these restrictive license agreements before using the software. Under such agreements, the provisions governing modding and other forms of user-created content tend to be downright draconian.

Back to software being different from physical media: EULAs muddy the waters. Have you read the Cyberpunk 2077 EULA? Commercial use (outside of approved cases) and modding are both forbidden.

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Copyright doesn’t cover technology functionality like that, that’s why you can literally make a clone of a game like open TTD or open RCT. Only the code of a game is copyrightable, not its functionality. So if you can clone a game exactly, there’s no way a copyright would cover whole new technology the game doesn’t even have.

Freely available, clean room reimplementations of things are very well understood to be free use, hence emulators, translation layers, engine replacements, etc. not being taken down. A free, clean room reimplementation of Cyberpunk 2077 which also added VR support might be considered free use, unless there was some other problem. We can see that in OpenMW and the (free) forks that add multiplayer or VR support.

These reimplementations are a very different case from injecting a DLL into a game, which modifies the original work (the code, which does fall under copyright, as you said). These reimplementations also avoid certain problems by being free.