If Elon Musk open bitcoin casino would it overtakes Stake.com easily?
It would depend on the money he decided to invest in the casino, the target public and whenever he decided to register his business.
He would already had a good advantage thanks to his status as pop culture personality even in the crypto currency community, with all the money he has at disposal it would only take good management for him to have the biggest crypto casino in the world, In my opinion.
Elon musk is the richest man in the world with a net worth of over $245 billion, and cofounder of several successful companies all around the world (Paypal, Tesla, SpaceX, and shitcoin such as Dogecoin, Babydoge). So if he eventually owns a gambling casino, there is a higher tendency of it doing far better than all existing casinos, since he already has the funds to launch and organize effective adverts for promotions. And just like what @Adbitco said, it's policy about KYC will also determine the crowd that will flood to his casino.
I don't think Elon had anything to do with the creation of Dogecoin or Babydoge, as far as I know. He only endorses Dogecoin saying it is his favorite cryptocurrency, even over Bitcoin.