I think electrum as a web wallet
a web wallet (just like its name) is a wallet that is on the web. in other words wallets that have a website like blockchain.info coinbase.com xapo,....
electrum and wallets like that are called desktop wallets.
you can use some well reputed mixing services like bitmixer and cryptomixer to mix your coins while sending from coinbase to electrum or other web wallets.
I doubt that this is really necessary. you are not doing anything illegal while playing on gambling sites. the only problem with coinbase is that they say you can not use our wallet to gamble so direct deposit and withdrawals will be problematic.