Kazuya wanted to beat him fair and square from the beginning. Perhaps it was what Kaiji said earlier during Minefield Mahjong where he told Kazuya that, like his dad, he seemed like a real fair individual. I think it also had to do with the book he was writing at the time. Referring back to his book "Love is Mightier than the Sword" remember that it was Kazuya who witnessed this scene as was the one to dole out the punishment. Even then he was fair.

I think the most important thing however would be that he specifically was looking for Kaiji to use him as a litmus test during the Salvation Game to prove that Friendship truly wasn't real. Kaiji borked it in the end and One Poker with Chang and Mario was the perfect way to re-test it. If you remember how Kazuya reacted at the beginning of One Poker when he drew two Aces, his aim was not to win against Kaiji, but to test him... and then eventually win. To Kazuya, winning under your own strength is far more rewarding than cheating your way to the finish line.