*bangs head onto desk*
Seriously, y'all. I don't believe Dorian is an alcoholic. You are reading way too much into this stuff.
I've got doubts myself. He certainly uses it as a crutch, which is definitely an issue, but lower on the panic scale. He mentions drinking mainly at crisis points: when Alexius went off the rails, after the confrontation with his father, if the Inquisitor breaks up with him, and so on. He lives in a medieval setting - yoga and jogging aren't acceptable methods of stress relief in that world, and the pub/bar/tavern/whatever probably would be the place people would go to blow off steam or escape (admittedly, as a noble, Dorian may be used to having other hobbies or diversions- perhaps that's part of the problem?).
Stealing alcohol isn't a good sign, but people's main concern appears to stem from the fact that the game gives the impression that he drinks alone - he's not a social drinker like Bull, Sera or Varric. I don't like alcohol at all, so I'm not the best placed to comment, but most people I've met will excuse a lot of drinking if it's done in a group, only to panic if a colleague or friend mentions polishing off a bottle of wine after a break up. It's "a good night out" if you and six friends end up vomiting over the pavement, but "a desperate cry for help" if you drink that much alone. That's probably why Bull and Sera don't get the alcoholic label so quickly, even though drinking with Bull is not an exercise for the faint of heart (or liver).
The other character who's a suspected alcoholic is Fenris, for much the same reasons: he's steadily working his way through someone else's wine cellar, he's notoriously introverted and solitary, and we actually see him drinking rather than just hearing about it. But again, it's mainly at crisis points...and let's face it, that's where most Dragon Age player characters keep meeting and interacting with their group. The action's condensed, and more mundane things get left out, so we don't get many opportunities to see Dorian lying out on the grass at Skyhold, filling in Sudoku. Which is why the chess scene with Cullen is so nice, even if it's not Dorian's scene.
You can spin it both ways - Dorian doesn't black out, he's not ashamed of enjoying a glass of wine, it hasn't nuked any of his relationships, and it hasn't prevented him from doing the important stuff (all signs of alcoholism). He likes annoying Josephine possibly more than he likes drinking (listen to her talking to the messengers in her study - Dorian is a massive pain in the neck!), and Blackwall doesn't like Dorian - of course he looks for ways to hurt or undermine him. On the other, we don't know for certain that any of these symptoms didn't happen and we certainly don't know that they won't happen in future- who'd have pegged Alistair as a drunken vagrant?
Short version: I think my Quizzy would probably be at the stage of "I know your dad's an (insert expletive here), but lay off the wine, Dory - let's go torment Cassandra instead," but wouldn't have licensed Varric and his "DON'T" sign to stage an intervention quite yet.