Something doesn't get to be "A Hamlet" just by having a son avenge his father. That's an incredibly shallow reading of the original story and a boring basis for any new adaptation into another story. I'm looking at you, Akira Kurosawa and Allers & Minkoff.
In order for a story to be "A Hamlet" you need at bare minimum:
- A son whose father is murdered.
- The murderer usurps the father's role.
- No one but the son sees a problem.
- The son seeks vindication through psychological manipulation.
I think you're a sinner if you don't also include Ophelia, but I don't think she's load-bearing for a plot to be recognizably Hamlet.