"So you say you're a human who was transformed into the shape of a cat, -and- you can use magic?"
"And you? You're a time-traveller? We may just be able to work something out here...."
And really, at the point where both of them realized the other had something they wanted, the match just didn't seem important anymore. Lynx decided to forfeit so he use his newfound insights into time travel to go back in time and make it so the Chrono Cross scenario writer died a horrible tragic death before finishing his work.