If I cancel Watcher in the Woods with A Test of Will and the current quest has Battle/Siege, does it still gain surge? I ask this because the "gaining surge" part is included within the "When Revealed" paragraph
Regarding Cair Andros, the card says "If blah blah, this card gains Siege", as opposed to "While blah blah, this card gains Siege", so it makes me question what happens if my threat drops below 37 after this card gained Siege... does it loses Siege¿?
1) If you cancel the treachery it will not Surge, because the part that grants it surge is in the When Revealed text and gets canceled.
2) I would think that the quest card loses Siege if you drop your threat back down under 37.
Pretty sure the Watcher will not get surge since, as you point out, it is inclusive to the "when revealed" portion of the card as opposed to it's own keyword.
I could see that behaving either way though I feel like it was intended to only gain seige "while" someone's threat is 37 or higher.
I agree with all of this. Surge is only uncancellable if it's printed above the When Revealed part.
I think that quest card is something you constantly check for so if there is no longer a player at 37 or higher the quest card does not gain siege and remains a normal quest.
Is there a this definition for gain in this game?
Is there a this definition for gain in this game?
Yes... but only in regards to resources 
While I agree and think that the surge can be cancelled since it is within the When Revealed portion of the text, we do have a precedent that you cannot cancel some effects that are within the When Revealed text.
There are numerous encounter cards that say "This effect cannot be cancelled" within the When Revealed portion of the text. Obviously, it is fairly clear that you aren't supposed to be able to cancel this effect.
So while I agree that Surge should be cancelled in this type of example, I don't think we can say for certain if the developers haven't clarified.
We're pretty certain about this. Nothing in the text says 'cannot be canceled,' so you are free to cancel all of the text the follows the words 'when revealed.'
We're pretty certain about this.
I don't think we can say for certain
So we agree