Simply put, the game is this: always trying to win the biggest amount of money to always have the chance to turn things around. I understand that the main question in the discussion is: if you had infinite money, would you still continue to play? I don't think I would, because we bet for money, but not everyone, there are some who would try anyway.
The possibility of winning money is the main goal of gambling. If people played for other reasons, they wouldn’t attach a financial element to it and would play just for fun. In that case, gambling would be more like board games. I mean playing without involving money but still experiencing excitement is absolutely possible. Board games are a clear example of that. Or online multiplayer games. But gambling, in its essence, is about money. So if you remove that factor, there’s nothing left that keeps the player there.