But how is this different from wallets like Mycelium or Electrum? We import private keys in these type of wallets too. I think as far as gambling site is taking input in front end then it is safe although I am not expert in this matter.
You should have a basic understanding on the difference between web wallets (hot wallets) and software wallets like Electrum, Bitcoin Core, Mycelium, Bread and other trusted wallets. Desktop/mobile wallets offer full control over your coins and your keys are never stored anywhere apart from the devices. If you have your devices offline, your keys never leave your device and can be used to hold large sums of money. Whereas on the other hand, web wallets like blockchain.info, greenaddress stores your private keys online and these keys were generated online. Your private keys are exposed and you have a higher risk of losing your money if you are connected with web wallets. You are not the only one who has control of your keys and they are online always.
Most of the gambling sites use cold wallets similar to a cryptocurrency exchange and when you transfer your coins to the gambling site address they move to the cold wallet and balances are updated in front end database. Gambling sites doesn't create a separate wallet for each user AFAIK and they depend on a particular hot wallet where they receive funds and they are transferred to cold wallets once they receive them.
Gambling industry is highly regulated, but some alt based gambling sites which run on TRON and EOS blockchain do provide a solution for decentralized gambling casinos. I don't recommend gambling sites which I have never used (since you might have a risk of losing money) but I would rather advice you to stick onto famous and trusted gambling casinos like PlayBetr, FortuneJack, MintDice, CryptoGames and Bustadice instead of risking your private keys and money with a untrustworthy casino.