Superficially the play is about revenge, more precisely delayed revenge. I think this is largely because that is how Shakespeare had received the old Amleth legend. Within this framework is where Shakespeare actually applied his artistry.
I am going to disagree with your theme. Though, I think you are on to something. Hamlet is an adolescent facing the duplicity and reality of an adult world. I don't see existenialism or government as the issue. Claudius is the source and spread of ill in the play. Not because he is the government but because he is not the rightful heir to the throne. He is a usurper.
To follow that, the play is to deterministic for existentialism. Hamlet has a role he must fill, rough-hew it how he will. I think Hamlet's anguish comes from certain basic realizations such as virtue, honor and nobility are not innate. That life is a double edge sword. Ambition is both good and bad. The line between love and lust is not a clear one. Image can be reality.
I do agree with your assessment of Hamlet.

