I think it all depends on the degree of seriousness of our relationship. Moreover, I would take into account how bad an impact gambling would have on me. That is, if I realized that she only wants the best for me, then I would definitely listen. to her.
A girlfriend that doesn't care for you will ignore whatever you are doing may it affect you positively or negatively. If they aren't serious they will not spend their precious time advising you to fix things on your end like advising you to stop gambling or stop anything that will affect you negatively. The fact that they are concern about your gambling activity, the girlfriend is pretty much serious about your relationsip.
I can't agree with you completely. You see, her anxiety can be caused by both sincere care and love, as well as a desire to control everything and rejection of hobbies. Agree, there are relationships where one of the partners strives to fully control the other, literally not letting them breathe.