If you don't want to admit that this movie is a musical, then why did you put up tens of millions of dollars for Tim Burton to make a musical?
Seriously, though, I know that a lot of trailers for musicals do their damnedest to disguise the fact that they're musicals; it's not just this one. The thing is that I don't believe it works. It would be one thing if these trailers made the movies out to be incredibly interesting non-musicals, but they don't; the new Sweeney trailer (the first without any singing whatsoever) doesn't make the movie look like a particularly exciting period horror story.
It seems to me that the best way to do a trailer for a musical is to show brief excerpts from the musical numbers. That's basically what movie musical trailers did in the days when movie musicals were common; they wouldn't show a lot of any one number, but they would show just enough to make the songs, and the performances, a selling point (sort of anticipating those TV commercials where we hear one line each from all of Performer X's greatest hits). Of course this might not work as well when you're making a musical with non-musical performers, but I still think it would work better than pretending that a musical can ever look like a good non-musical.
I mean, Grease is not a great movie (though I think it was a better movie than a stage play), but the trailer made it look like a musical, and played up the songs as part of the appeal: "Everything that makes a musical unforgettable." That's how you market a musical -- don't act ashamed of it.
Update: I realize, of course, that the songs from Sweeney Todd are a tougher sell than the songs from Grease, but that's an argument for making a trailer that makes the best case for the songs. They could have done a trailer playing up the comedy songs, or plugging "Not While I'm Around" (which never became a pop hit but which Prince and Sondheim were clearly hoping would be this show's "Send in the Clowns").