The original game arcs that were transferred to the anime are complete.
However, there exists a special separate ending chapter for Higurashi that only appears in the japanese ps2 game. Fortunately, I own it, and was able to translate enough to give a brief summary. I'll try to keep to what is different.
1. Rika is revived after the Everyone Dies chapter. She can't find Hanyuu anywhere, but she does remember Takano Miyo is the mastermind behind her murder.
2. Rika weighs her options, and decides her best course of action is to try to tell Keiichi what's going on. (That is, how she is killed every year, the lead up is Tomitake dying and Takano 'disappearing', etc. etc.)
3. Keiichi believes her story and vows to help her to the end.
4. Rika and Keiichi realize that after Takano, the people who are most threatening to the happiness of Hinamizawa are Mamiya Rina and Houjou Teppei. Rika suggests they let Rina be killed, then Keiichi can rally support for Satoko like he did in the Everyone Dies chapter, but Keiichi says there must be a better way.
5. Keiichi and Rika approach Shion and Kasai. They tell them everything about the situation with Rina and Teppei. They agree to lock Rina out of the club she works at so Rina can't steal from the Sonozaki's. Kasai also warns them that Rina is connected to Rena's father.
6. Rika and Keiichi attempt to confront Rena to let her know Rina is targetting her father. Rena at first denies this, saying Oyashiro-sama came to her in a dream and said her father should be allowed to find happiness in re-marriage, but they snap her out of it.
7. Rina is killed by the Yamainu, who they hope to make it look like the Sonozakis have done it. Teppei returns to Hinamizawa. Rika, Keiichi, Akasaka, Oishi, and Shion intervene to take Satoko away, but Satoko is already beginning to lapse into Hinamizawa Syndrome.
8. The Watanagashi festival occurs. Takano confronts Tomitake as always, and it's unsure what happens to him. Keiichi receives a phone call from Oishi saying a person's corpse was found after the festival: Houjou Teppei's. Takano also officially goes 'missing'.
9. Most of the normal events that happened in the anime happen. Oishi/Akasaka/Dr. Irie/the Sonozaki's all team up and cooperate; Rika is 'pronounced' dead as a bluff; Shion discovers Satoshi is being held in the Irie institute, etc. The difference here is that Shion overhears Satoshi is being held and brings a gun to the clinic to force Dr. Irie to show him to her. They calm her down and it's decided Shion will have 'killed' Rika and Oishi 'arrests' her.
10. The Yamainu kidnap Satoko from the Irie institute. They attempt to use her as a bargaining chip to bring Rika out of hiding. Dr. Irie is also taken as a hostage.
11. Rika and Keiichi meet Takano in front of the Furude shrine. Rika and Keiichi think they have Takano beat: because it's been so many hours past when Rika was publicly announced as 'dead' the Yamainu don't have enough time to sterilize Hinamizawa anymore under the guise of 'containment'. They try to convince Takano that her best strategy would be to give up, and try to live with them peacefully.
12. Takano reveals she has a backup plan: she's managed to create an airborne version of the drug that triggers a lethal level of Hinamizawa Syndrome. Instead of gathering the town together and shooting them like she planned, Takano now intends to release this new drug into the air and kill everyone in the town's radius by triggering the disease, including the police who are investigating. (The Yamainu will escape by helicopter.) Keiichi, Satoko, and Rika react with horror much to Takano's pleasure. Takano announces that one way or another, Hinamizawa will feel the wrath of Oyashiro-sama.
13. Takano decides the kids have outlived their usefulness and tries to shoot Keiichi. Time stops right before she pulls the trigger, and Keiichi finds himself in a dream sequence where Hanyuu tells him to fight. When it's over, Keiichi finds himself able to move while time is stopped, and dodges Takano's bullets. He grabs a smoke grenade off the belt of one of the surrounding Yamainu, and the kids manage to escape.
14. After some delay, Satoko leads the pursueing Yamainu into a series of traps made by her. The Yamainu fall one by one, Rika hides out in a shed while the rest of the kids go to meet up with Mion, Rena, et al. Hanyuu comes to Rika and reveals she wasn't hiding from Rika, she just wanted to prove she believed Rika could be saved as well. Takano, meanwhile, is livid because of her failure, and orders Okonogi himself to go track the kids down and kill them.
15. Okonogi finds Rena, Mion, Keiichi, and Satoko. He praises Keiichi for his leadership, and Satoko for her traps, but announces he can't give up that easily, even if the Yamainu have no real interest in Rika anymore. Keiichi knocks him unconscious.
16. Shion leads the police to the site they suspect Takano is hiding with their car. Kasai acts as a sniper and they bypass a Yamainu road-block much like in the anime.
17. Takano and Rika meet face-to-face. Takano has taken some bad injuries from (I assume) Satoko's traps, and is hell-bent on killing Rika even though she knows the game is up. Rika tells her that she doesn't hate Takano, but she realizes she envied Takano because while Takano struggled hard by herself without anyone to help her, Rika needed to surround herself with her friends and allies to survive. Takano announces she hates Rika for the exact same reason; she struggled all her life just to get her grandfather's research noticed while Rika is loved simply because she's Furude Rika. Keiichi and Hanyuu show up and prevent Takano from attacking Rika. Hanyuu (who is now tangible, for some reason) and Rika both offer to forgive Takano. Takano considers it for a brief moment, but then states quite lucidly that she's already killed many people to accomplish her research, including Rika's parents. She won't be forgiven by the rest of the world so easily.
18. The Banken finally show up. They see Takano, and one soldier opens fire. It looks like Takano is going to be killed, but Hanyuu jumps in front of the bullets at the last second.
19. The Banken announce Takano is to be arrested, but Tomitake shows up and declares Takano has likely contracted Hinamizawa syndrome, and thus is not responsible for her actions. Meanwhile, the police finally arrive. Oishi realizes this is over his authority, and asks Akasaka to ensure things are tied up.
20. Hanyuu dies in front of Keiichi and Rika. She tells them not to feel sad, because she's the god of Hinamizawa, and it's her duty to protect everyone and make sure they lead happy lives. The rest of the club members are reunited, and Rika decides to live life like Hanyuu wanted her to do so.
EPILOGUE:
1. Satoshi is cured by Dr. Irie. He returns to Shion and Satoko with the bear he promised to give her long ago.
2. Keiichi continues to teach Mion and Rena at school. It's unlikely their love triangle will be resolved anytime soon.
3. Takano begins to recover at the Irie clinic. She's visited by Tomitake.
4. Akasaka, Oishi, and Oishi's partner Kumagai play Mah-jong together.
5. Rika and Satoko continue to live together.