IANAL and am not presenting a legal opinion. What I am speaking about here is based on numerous conversations I've had with lawyers in the "IP" (sic) field.
How do you define an entire work?
I've been told repeatedly that one game == one work. Others have said that it was unclear and I'd have to research legal precident (case law) on the issue. Nobody has said that it's a matter determined by the author or that they are more than one work. In the end it comes down to a judge's decision on a specific case, but overwhelmingly judges favor the author(s) who's work is being extended/modified in copyright infringement cases, and because this is known it almost never gets to court.
The issue of code and content is no different than the issue of patches or libraries. Labeling one part "code" and another part "content" changes nothing, both are software and both are part of the same work - the game you're releasing.
Consider even on a technical level how arbitrary the "code" vs "content" labeling is; code is rarely (if ever anymore) direct machine code, it's compiled or interpreted instructions which are processed by other software and instruct that other software what to do. Content, lets take a graphic for example, is processed by other software and instruct that other software what to do.
Game engines, and more specifically game code, are not "game browsers" - at least I've not seen a modern one that is (ScummVM is not modern). The pieces of your content are usually labeled and have parameters specific to the game code you're running, ie FighterIcon1. Of course you can swap out FighterIcon1 for another FighterIcon1 with the same requirements met and have it run, but you could also replace one of the program's FighterDamage function with a replacement that has the same arguments and return types in order to change that software's behavior.
As the copyright holder, it would be my prerogative to
license either how I see fit, and I see nothing in that license that
states I must license my other works under it, just because I choose to
distribute them together.
You are correct, if you were the sole copyright holder there would be no issue. The GPL does not restrict a sole copyright holder in any way because the copyright holder needs no special permission (a license) to do anything with their own work.
However, this is almost never the case. GPL licensed work often extends work held by several, sometimes even hundreds, of different copyright holders. Any or all of them can challenge your right to use their work on the basis of license violation and thus copyright infringement. Work is not licensed under the GPL in the spirit of allowing 3rd parties to make derived work effectively proprietary.
I can tell you that if someone tried to pull something like this with our engine they would receive a notice of AGPL violation with a 30 day window to rectify the problem.