JSON of the last thread, and hashes of JSON files retrieved from the /gg/ archives before I explained the game.
Thank you to everyone that made their guess. In short terms, the answer to the game is this: "It guards against tampering of past threads by relating cryptographic hashes of each thread's contents."
Posting JSON archives creates a cryptographic relationship between the contents of threads. Since each thread contains the SHA-256 hash of the previous thread's contents, the final SHA-256 hash can be assumed to have been constructed using the complete binary contents of every previous thread, including the SHA-256 hash of any files in each thread.
The primary consequence of this relation is non-repudiation of every past thread for which the hash has been posted. This also acts as a significant improvement of offline archives, where each thread acts as a cryptographic witness of the contents of previous threads.
As pointed out multiple times, this is not a complete archiving system: it is not capable of verifying that each thread's contents have even been posted on 8chan at all. This mechanism is complementary to other archival mechanisms. From an attacker's point of view, the effect is this: a forgery cannot succeed simply by altering a single thread. A forgery has to proclaim a competing history of threads to be successful in deception. Silent forgeries are made effectively impossible when paired with any other archives, although users still have to be attentive in obtaining, preserving and authenticating their own archives if they wish to have full assurance in their own copies.
Now that the mystery game is over, let me say that I intend to go further with a similar system soon operating on the same principles, with the JSON archives acting as a substitute mechanism until development is complete.
With GamerGate having started more than a decade ago I think it's time to state the point of the game properly, even if it is preaching to the choir:
You have consistently demanded honesty by dutifully archiving each thread in sequence. A small change in the archival procedure was enough to establish cryptographic non-repudiation properties for the archives.
Governments and other powers continue to humiliate, torment, manipulate and deceive while exercising power and claiming dominion. Such powers continue, with unrelenting chutzpah, to lie and cause chaos with one hand while falsely claiming to be a refuge for order, peace and clarity with the other hand. Wherever possible, they have preferred to lie and to preserve their ability to lie and have done so in spite of many already-existing widespread tools and mechanisms to guarantee honesty.
The JSON archives are one more such mechanism: an accidental ad-hoc mechanism re-purposing the storage de-duplication technology sometimes referred to as content-addressed storage. This system demonstrates that not only do such mechanisms exist, but they are so ubiquitous that they've even occurred accidentally, with zero dedicated development, waiting to be used.
Despite all the criticism that GamerGate receives, it is a simple fact that you have sought and demonstrated greater honesty than has been returned to you.
It is my conviction that, if you continue this uphill battle with the truth in mind, you will see a worthwhile resolution that justifies the troubles you have suffered and you will have the opportunity to see that truth leads to beauty and meaning. As a long-time lurker, thank you for your dutiful observation over the past ten years.