The problem with chess is that the shortest possible game is already known, where Black wins on its second move. In chess notation, it's 1.f3 e5 2.g4 Qh4#.
If I have to explain it, it's roughly as follows : White moves the pawn on the F file (where the white-squared bishop is) by one square, thus moving it to the f3 square. Then, Black moves the pawn on the E file (in front of the king) by two squares. Then, White moves the pawn on the G file (in front of the black-squared knight) two squares ahead. Finally, Black moves the queen to the h4 square which is checkmate. Here's what the checkmate looks like.
http://yfrog.com/htcheckmateintwoj (Alternately, White can move the F pawn by two squares, and Black can move their pawn by only one square, it's the same thing in the end.)
Obviously, a regular, strong chess engine would never fall for something like that (no strong chess engine would play one of these moves early in the game because they aren't good to begin with), but in a TAS, who knows what can happen...
Any chess nut such as myself knows that. However, seeing "playaround" games would be interesting, at least to me. I'm sure someone can come up with a lot of creativity, whether the moves are actually good or not. In video games, such as on the NES or whatever, chess video games tend to be of a low playing level, since it's aimed at kids after all. Others have difficulty levels. It would be fine to have a category where the computer loses like on the link I provided (shortest possible checkmate), regardless of difficulty settings, but if it's just that, it's not very interesting. It would be nice to see something more, because personally, seeing a TAS end like that with nothing else would leave me on my appetite. Chess games would be good for playaround runs however. Well, for those that know chess well, that is.