I honestly thought this was hilarious! JKF?? Haha good stuff! I am not sure if you're familiar with Banjo Kazooie, but this reminds me of something if Banjo Kazooie made a interrogation scene where you played as Banjo and interrogated Kazooie for stealing something. Like if they could talk, I feel like this could be them.
I feel the atmosphere is just right with the setting of the game in how it is supposed to goofy. I think the interrogator's dialogue pace may be a little slow, but I am probably not sure if that's just part of his character.
Your interpretation of using the theme as a mystery game was pretty good. I like how you used it directly without making the game feel contrived. It worked well.