On the surface, it is a tale about revenge, that ends in devastating tragedy for most of its main characters. Think of all the people that died: Polonius, Ophelia, Claudius, Gertrude, Rosencrantz, Guildenstern, and finally Hamlet. That sure is a lot of death. And because Hamlet's main purpose in the play is to enact revenge, it does fit under the category of revenge.
However, there are many underlying layers, all connected to Hamlet and his inability to act. The entire play consists of him moping about, whining, hesitating, pondering life and death, making excuses--all when he could have enacted revenge from the very first suspicion of Claudius. So, the play is more a commentary on inaction, on procrastination, on how "the mind is its own beautiful prisoner", trapping people in analysis and logic instead of determination and action. Hamlet overthinks, overanalyzes, overponders, oversteps bouds of decency in order to more fully ponder the situation, and all of this is what really leads to the tragedy, not his pursuit of revenge. It is useful to also consider those elements as you decide how to think about and label the play.