Your two definitions are not far from each other; the desire for more is not just for the money but can also be the desire to get more status, to feel satisfied that you are on top of it, or anything that leads to the person not being satisfied and needing more victory and more money. Anything that's beyond just a normal one-time winning and moving on can be regarded as greed if you ask me.
I wont agree with you honestly. You can desire for more and not feel satisfied even when you get what you want. This is how the greed of many persons increased significantly. While there are people, when there greed pushes them to crave for more they become satisfied if they get what they want.
Perhaps what you fail to understand is that, we speak of greed but there are different level of greed. There are many folks with greed and desperateness when it comes to gambling.