It's not a remake, it's more based on the book and stay true to the original title. Not only to mention that it's not a musical either. It has the same storyline, but not the same as the original. The original cut a lot of the story out of it due to the songs.
By the way, the author hated the original. That's why he never sold the rights to the second book, Charlie and the Great Glass Elevator. I noticed that they featured the Great Glass Elevator in the new movie, as least I got that impression from the preview. In the original, it was a sort of weird-looking helicopter or something.
