does anyone know how to judge such an event?
Pretty simple. Each player is given one credit, and their names drawn out of a hat to choose order per game.
Then they play as best they can on that one credit, and their scores recorded.
At the end of the day, normalize all the scores (with some games, 10,000 points is a high score, in others 10,000,000 is a low score), add them together and pick a winner.
If you don't like score normalization, then use per-game rank. First place is 5 points, 4 for second, and so on.
Up to you if you want to allow a practice run, or "best of 3" attempts, etc.
Fighting games of course are much easier. Just like any other sporting tournament with standard single/double elimination rules.