If you do not have the intention to save the wealth, you will lose all your winnings by risking them again in another gambling bet.
Only a mentally strong person who has control over emotions and have money management skills would be the real winner here and will become rich eventually.
I don't think that they have anything with a healthy mindset, but a unhealthy mindset because people with unhealthy mindset often tend up losing the all won money. Those people basically think that they will be able to multiply their earnings many more times and as a result they will be rich. However, in reality those people are the losers because after doing many bets in gambling they will end up losing everything they have ever won from previous bets.
It's true that a person who is mentally strong can earn and withdraw money many times from gambling sites because such people know their limits and they also know that they can't be lucky all of the times. Those people will always take their initial investment back and then do more bets with the money that they have earned from betting. I also believe that such people are mentally strong because someone who can control his/her emotions very well is considered as a mentally fit person.