A few years ago, I came up with seems to be a similar concept, and it would've aired late at night (11:00 hour or later), with a revolving lineup of puzzles and word games (think the call-in-and-lose shows of the mid-2000s, except in-studio). If done right, I think this could be a lot of fun, NBC or not.
When I read the concept, I thought either Friday nights or even late night after the talk shows (Poker After Dark's timeslot) or Saturday Night Live. They have some weird celeb show on after SNL now.