Justice Tingling, if I read the ruling correctly, basically said that the Health Board hasn't the legislative authority to regulate this kind of thing unless New York City Council enacts legislation allowing it. I'm no lawyer, but I've no reason to expect Tingling has this wrong.
I'd also expect that if Bloomberg really wanted the ban and thought he had the votes on Council to do it, he'd be trying to get the ban through Council rather than talking about judicial appeals. If he hasn't the votes to get it through City Council, maybe it's because Swinburn's "power of the food industry" hypothesis, or maybe it's because a bunch of people in Brooklyn are fed up with this kind of nonsense and would punish their Councillors for it. I've not been following the poling on this closely; a quick Googling suggests that it's hardly a policy drawing unanimous appeal and that would have passed but for Big Sugar. Instead, there's a slim majority in opposition to the policy.
But Swinburn's all about the framing here: "public health versus private profit". Voter preferences don't enter into the story because they're all on his side, never mind the polling. Expect this framing to be used here when Swinburn's type push for similar policies here.