As a simple, clean telling of the storyline, this works. But sometimes it's very awkward. What I gained from the book (which is definitely not intended for my age group) is an interest in further discovery of some of Shakespeare's plays. Probably that is its aim for children, and I would suggest children 8-11. Would I share it with children? I don't know....
Shakespeare's plots are complex. Nesbit strives to include the necessary parts, which sometimes makes the mere facts the only inclusion. It also forces the mere facts to be swiftly told. There's a beauty that gets lost that even a child might notice. As a child, I think I would have not been attracted to the writing style because of that.
In an effort to give some of the flavor of Shakespeare, Nesbit included a few quotes. I appreciate the gesture, but sometimes it gives a very awkward flow, even in a single sentence. Shakespeare's language style simply does not flow into the modern English of Nesbit's time. It never will.
Some things just have to be enjoyed in their original forms. Updating and simplifying can't do them justice. In very few situations, it might be good and right.