Any Way the Wind Blows
“The mission statement of the Gold Saucer's founder, Godbert Manderville, states that all are welcome to seek employment at the Gold Saucer, regardless of race, nation, or creed. It's even said a kindly voidsent has joined their ranks after an aborted gladiatorial career. But who can withstand his gale-force nasal eruptions?
— Lodestone Gold Saucer page
Guide
Players walk around the stage area and find a place to stand, and Typhon will appear after a notification appears on the screen telling you not to move. Any players caught up in his Snort AoE attack will be blown off the stage, and points will be divided up between those players who are left on the stage at the end. This is a game simply based on luck.
That said, you have the best chance of winning by standing at the wingtips of the butterfly at the southern side of the stage. See here for reference.