It would be better if you have proof of how you are receiving your salary from your workplace. Or I think a bank statement of account should also be enough as an evidence. I think the transactions on electrum is not enough. Or are you paid in bitcoin in your country? If so, the gambling site customer care will ask you questions about it and they will still need proof from the company you are working from.
That's stupid to be honest. Why would a crypto casino that doesn't accept fiat money want their users to show them bank statement? There's a lot of unbanked people around the world who voluntarily or involuntarily do not use banks. There's a lot of youtubers who made money trading cryptocurrencies and they no longer use banks, just operate 100% on crypto credit cards.
Signing an address to show how much bitcoin you hold should be enough proof how much money you have. What if you're unemployed, but hold a million in bitcoin? Does that mean you have no right to play at a casino because you have no income? I know you won't answer that, but it's just that the stupidity of this rule is striking.