"The Tempest" is a Shakespear Comedy. A comedy according to BrainyQuote.com is "A dramatic composition, or representation of a bright and amusing character, based upon the foibles of individuals, the manners of society, or the ludicrous events or accidents of life; a play in which mirth predominates and the termination of the plot is happy; -- opposed to tragedy."
I see the play as a comedy because no one dies at the end. They all get on to the ship and head off to Italy as if nothing happened. The play also had lines like "I have great comfort from this fellow. Methinks he hath no drowning mark upon him; his complexion is perfect gallows. Stand fast, good Fate, to his hanging!" said by Gonzalo (pg 11-12)
To determine that a man is going to die by hanging and not somthing else is a little bit of Shakespear humor.