Sounds to me like he just wants to change the subject. In his mind, he acknowledged your concern, thanked you for it, and that's that.
All you have to do, really, is to say, "Listen, I've been thinking about what you said the other day about your drinking. I think we need to discuss this in more detail. It seems to me the amount your drinking could have a serious impact on your health. I don't want to have to worry about a serious but preventable medical issue down the road. Would you be willing to talk to your doctor about it?"
See what he says. If he gives you the brushoff, then you can see that he doesn't really take your concern seriously. And that, in itself, is a problem.