I think you have simply misunderstood how the game works. The word is not set at the beginning of the round, it evolves as it is steered by player and computer - it's not just hangman. Surely you must have noticed that you could control this, since you get the first move. Thus, you actually have a lot of control over the length of the word, by thinking of how to finish it. I think more advanced play involves cutting off the computer, rather than just let it play - which is really the essence of most strategic play in all games. In terms of theme, well, I find this a bit ungenerous. Considering this was a very strictly officiated game jam, I'm not suring your judging all the hard work that went into this quite in the spirit of your own jam. Your thoughts?
When playing it, I was under the impression that the word was set from the beginning and that it was like hangman, maybe I just personally wasn't able to understand that from the introductory text. I do think that strategic games like this would benefit from some tutorial but of course that's easier said than done with the time limit.
Just because I didn't properly understand the game doesn't mean I didn't enjoy playing it, I had fun and I don't think it's a bad game at all. Also remember I may be the host but I am judging the games just like everyone else - my rating has no more effect than yours. I'm just trying to give constructive criticism, doesn't mean you need to take it or listen to it.
And yes, I also liked the hats.