Heh. I've daydreamed this too.
Think it would be cool to focus on the drama, rather than recreating the "real experience of the real game."
ie, I imagine when you are inside the box, you'd have a third person camera showing you huddled. Camera panning around slowly. cutting to close ups of your haunted eyes. close ups of the hair on your arm raising. close ups of your fingers tracing the inside of the box. etc. Like an procedural movie that is telling the story of your tension.
+Maybe offer an overload of zany controls based on elements of the tension, that you have to overcome to work up the will to peek. golf-swing-style-sliders, quicktime event buttons, camera changes, and meters to hammer to fill up. etc.
Then when you peek, play a quick cut scene celebrating the power explosion of daring to attempt a peek.
And then switch into a first person view aimed the other box. Change the gameplay focus to picking up details of your opponent. Highlights, outlines, arrows and other UI flourishes flying off their box - all adding up to a puzzle of whether/when they are about to peek too.
To be honest, i daydream more about making a tool to make it easier to make the episodes (like the software South Park uses). So Kyle could produce more episodes (not sure how important it is to him to keep the washed out flimsy cut out aesthetic). or it could be a tool for the community to go wild with tribute ideas.
I make games (as day job and hobby), but in general i daydream about using Unity3D to produce weekly tv shows with a set of reusable assets (Unity and Unreal both seem keen on improving preproduction for high end hollywood studios/houses. but i think there's an overlooked opportunity to use these basically free tools to bring back the indie video maker community that youtube kinda killed off. Making short form narratives with drama, tone, story and structure - instead of following the current trend of streaming everything and just getting by on a cheery personality).