What knowledge do players get when Hangman is sent to another game using Side Quest?
This is silver-bordered land, so of course there is no &quot;real&quot; rule to cover this. As such, this is my interpretation of the interaction.
Hangman keeps all of the &quot;state&quot; of its mini-game, and Hangman's new Side Quest controller becomes the mini-game's gamemaster for the duration of the Side Quest. So Hangman would keep its originally-chosen word, Hangman would keep its +1/+1 counters, and all players in the Side Quest game would have access to which letters had already been guessed and what the &quot;progress&quot; of the mini-game is.
My justification for this answer is that I would expect a generic 1/1 creature with a +1/+1 counter on it to keep its counter when going on a Side Quest, and I would expect a creature that had gained e.g. First Strike to retain that ability when going on a Side Quest. In other words, I think that Side Quest keeps the creature in its current state.
From Mark Rosewater's tumblr:

magicwizardmageman asked: What happens if you augment a creature on a side quest?
It stays with the creature and returns to the original game. Same for an aura. If either of the games end, the Augment/aura goes to its owner’s graveyard.

This sounds like &quot;official&quot; justification that you try to keep the Side Quest creature as &quot;current&quot; as possible while moving it between games.