This is hard to summarize into a TLDR, but I'll try. The general summary: an anthropologist gets mired in a village during a timeframe where there is nothing to do but drink beer and talk; she therefore tries to tell the story of Hamlet. This is complicated by the fact that their culture has a different social structure, and a different model of the supernatural. In their model of the supernatural there are just witches, who are always male, who can create purely-visual hallucinations (called "omens", they cannot "walk" or "speak"), animate dead corpses ("zombies"), afflict people with temporary insanity ("madness"), and drown people. (Yes, nobody drowns unless cursed to do so by a witch.) The rest of this comment is a synopsis of the Hamlet variant they create, arranged into play order.

Much like we view technology, for these people witchcraft is not necessarily negative but can also be done for the good of others. King Hamlet (Hamlet's dead father) thus becomes the Omen, a (veridical and therefore good!) vision sent by some witch-elder who understood the truth of his death at the hands of his brother Claudius, but was afraid of Claudius' new power. (There is a brief confusion because in the original story he walks and talks, suggesting a zombie, but they settle on him being an omen and the original story was simply wrong about him walking or talking.) Claudius's two big sins are his sin of fratricide in the past and later a sin of afflicting Hamlet with madness. Notably when he marries Hamlet's mom the tribe basically yawns "yeah, and?" -- this is so obviously the right thing to do that they don't make any further comment; of course your brother marries your wife if you die, for who else is going to support her?

The tribe is okay with the nameless elder sending the Omen to soldiers and then to Horatio, and because Horatio is a "scholar" he is therefore automatically a witch, so it makes some sense that he can interact with the Omen. However the tribe is surprised that he does not refer the problem to an elder of the tribe as they need someone more wise to the dangers of witchcraft, instead referring it straight to Hamlet. But they go along with this, Hamlet sees the Omen which tells him that his father died from poisoning. However Hamlet is wise enough to know that false omens exist from evil witches, so he resolves to determine the truth of the Omen.

Now either events have to be reordered or somewhere before the storytelling, chief Claudius bewitches Hamlet with madness. Certainly he is mad when he interacts with his beloved Ophelia, and then he talks with his schoolmates and comes up with the idea for the storyteller friend they've brought with them to do a storytelling for Claudius which will determine the truth of the Omen. In response to this story, chief Claudius in his outrage and fear apparently continues to bewitch Hamlet with madness, but also sends Hamlet's mother to find out what he knows -- and of course he sends Polonius the elder (still Ophelia's father) to listen in, not trusting her to be totally honest with him. Hamlet's criminal audacity in scolding his mother is chalked up to madness. Then Polonius stirs and Hamlet claims that he sees a rat, but when he says "a rat?!" it is understood as a hunter's ritual warning to potential human victims standing in the way of the arrow, kind of like a demolitioner's "fire in the hole!", where if you hear a response you should almost certainly abort whatever you're doing. To save Polonius's reputation the narrator therefore explains that he responds "It's Polonius!" after Hamlet's "It's a rat!" but Hamlet kills him anyway because he's been afflicted with madness and thinks it's his chance to kill Claudius.

With Polonius gone you'll remember that his daughter Ophelia drowns. But since drowning requires witchcraft, the explanation given is that this was a treacherous act by Laertes (Polonius's son, Ophelia's brother), who was of course sent off to France where he boozed and gambled away his money irresponsibly. The explanation was that when he came back home, broke and in massive debt, he saw that his dad couldn't give him more money because he's dead, and he couldn't sell his sister for a handsome bride price because she's being actively courted by a chief's son and nobody wants to potentially piss off a future chief. So Laertes did the only thing he could do to raise a lot of money on short notice, afflicting her with the curse of drowning so as to sell her innocent body to malevolent witches to zombify as they willed. This is why he jumps into Ophelia's grave (to get her body out for the selling) and Hamlet jumps in afterwards because he senses the foul witchcraft afoot. Laertes therefore is pissed at Hamlet for robbing him of any benefit of killing his sister.

Claudius sees that Laertes is powerful enough in witchcraft to kill his own sister, and that is why he sets up this duel where both Hamlet and Laertes will kill each other, one by sword, the other by the poisoned cup of victory beer. The finale remains otherwise untouched and everyone dies, although again Hamlet's presumably killing Claudius out of madness instilled by Claudius, and we're never told how they reacted to a rival chief (Fortinbras) taking over everything afterwards.