I absolutely disagree with this.
If you are able to have savings after all living necessities, you can be using not more than 1% of your income on gambling. No need to think about the budgeting like it is something special.
I think the reason on why personal budgeting is important focuses more on allocating a specific portion of your income primarily for gambling.
Without any kind of budgeting, you run the risk of overspending and overconfidence- thinking that you can afford to spend more in the process. On the other hand, if you designate a specific portion of your income to gambling, once exhausted, you are somehow compelled to stop at that point.
Regardless, however, everything revolves around proper discipline and decision-making especially when you are at the point of losing continuously. Even if you have all the money in the world; or if you have allocated a portion in gambling, without any discipline then everything would be immaterial and futile.