It depends on what you liked about the murder mystery series: Whether that be the suspense, the death, the characters, the editing, winner-takes all, or the solving of the mystery.
If you want an overarching mystery with some game-like survival kinda stuff, the death game genre would be the type for you. In that case, here are some recommendations:
Higurashi When They Cry/Umineko series: the renowned visual novel murder mystery comparable to the likes of Agatha Christie. You can watch this as an anime or audiobook or play the visual novel.
Agatha Christie has a few works that keeps pace throughout the whole book (like And Then There Were None or Murder on the Orient Express) but many of them fall into having a lot of exposition. I'd suggest watching the movies instead.
For games, the Danganronpa games would be the closest. The Danganronpa: The Animation is just an anime version of the first game. The second and third games (as well as the other franchise things like the other animes which takes place between the second and third game). You can watch summary youtube videos or watch playthroughs if playing the games/solving the mystery is not your jam.
If you like that and enjoy the process of solving, you could play exclusive murder mystery games, like Ace Attorney or Zero Escape and then branch into more niche (but better) or niche (and short/specific) games, like Return of the Obra Dinn, Your Turn to Die, etc.
Now, let's go back to anime: I think for non death game anime, Angel Beats and Mirai Nikki falls under the same sort of plot progression of people --> mystery --> ending, though I would not recommend Mirai Nikki, lol.
Now, if you liked the characters and then the big brain ideas instead, World Trigger would be your pick. While there is less gore and deadly stakes, the author makes use of a power system called Trion that enables the characters to fight nonlethally with a lot of strategies.
As for the really good death game anime/mangas, I would recommend Liar Game (kdrama/manga). This is very much the mainstay example of the genre. Some others include Alice in Borderland (manga), Kaiji (anime or manga), Kakegurui (manga) and Tomodachi Game (manga).
Detective Conan or Kaito Kid also work. Specifically, the Kaito Kid anime is pretty good at remaining episodic but lighthearted (about a magician doing heists), whereas Conan is a binge of really short murder mysteries.
Finally, Twelve Suicidal Children (Japanese movie, manga) is extremely good and falls under the vein of recommendation. It has a very powerful message.
Okay, now it is time for me to comment on what the other people recommended (that I have watched/read).
Promised Neverland is a great pick for something similar that you can watch as an anime. It is about a group of children in an orphanage, but there is a larger mystery / thing at play.
Death Parade does have games + death down, but instead of it being a competition, it is smaller episodic games that try to explore human condition.
Akudama Drive is fine, has great art and is more in line with a battle royale kinda game, but has fun characters and a quick binge. If you end up liking this, I would also recommend Juuni Taisen (anime) and Battle Royale or Btoom! (manga)
I probably forgot some things (lol), but feel free to ask additional questions / share how you liked any of these anime, and I would love to talk about it! (I don't check this site often though, lol).
