I don’t received this kind of email on my Bitcasino email so far. But the comment of the user above is legit and they are connected to each other that’s why you can see the similarities on the format of the casino and games offered by Bitcasino to Livecasino.
You probably didn't receive it because they are sending those invitation emails only to users registered on one casino but not the others. It doesn't make sense to send an invitation to join a casino that you're already registered at.
Anyway, you're totally right. OP and everyone else should be careful when receiving such emails and have to make sure it's legit and has been sent from the casino's official email address.