Yes, gamblers should take full responsibility just like shopaholics, alcoholics and other people with addictions. If we start dividing this responsibility between those who advertise (of their product which, when used in reasonable quantities, does no harm) with people who consume it uncontrollably and face unpleasant consequences, we will harm all parties.
Still, gamblers have to be held accountable because it is their risk of becoming addicted. But sadly, not many can realize this and are drawn even deeper into gambling. I think this is a shared responsibility between gamblers, advertisers and casinos but I don't know, it seems that casinos and advertisers keep going without thinking about the fate of gamblers who are addicted to gambling.
How can this be done from a practical point of view? For example, you are a casino and an adult player comes to you and plays. What do you need to do to fulfill what you propose? I see some ideas but they are directly against the rights of the player and are an invasion of privacy, etc. I think it's easy to say "you have to be good and think about others" but in practice these ideas are either unrealizable or turn into something terrible (totalitarianism).