"Sober" in this context means "having overcome a dangerous alcohol habit/addiction". Pretty standard alcoholic terminology. Furthermore, much as they might enjoy a drink, alcoholics who have "gone sober" MUST abstain, as alcoholism is seen as lifelong once acquired and the risk of lapsing into self-destructive behavior is too great after even just one drink.

"Teetotaler" usually refers to a person who abstains from alcohol on general principles (does not like the effects, taste, thinks it's a moral vice, etc.).