Don't know how to detail more, but basically I'm looking for death game mangas done right, which means good story, not axed, preferably finished already (because these have a tendency of going on translator's limbo).
Don't really know any examples other than Kamisama no Iuutoori

Jinrou Game a perfectly competent, if simple, example. The sequel is fine too.

Tomodachi Game not a "death" game, but has similar tropes. Ongoing, though.

Uhhh I don't know if this can be considered a death game but
Imawa no Kuni no Alice

A fellow Kamisama no Iutoori fan? Here I have a collection of death games, some lighter than others.

(The ones already recommended are good too, especially Imawa no Kuni which has a sequel now)

Gantz-- not a personal favorite, but it's a classic. Boy dies, has to play death games with others as dictated by a floating ball.

Life is Money-- definitely a lighter one, I think, but still fun. MC needs to get money for an operation for his sister and ends up playing a game with high stakes

Doubt/Judge-- two manga by the same author (theres more but these are the two I read). First is about a cell game turned real where they have to find the wolf among the rabbits. Second is about kidnapped people need to escape by voting each other off.

Aphorism-- another lighter one. Kids go to school where they have to fight monsters with a single word of power. Things do not go well

BTOOOM-- people are dropped off on an island and have to kill each other via bombs

Kings game (Ousama Game)-- two stories, but the better known one I think is a set of high school students get mysterious texts demanding people obey them. They start off light, but as they escalate people start dying. Refusal to do the task means death, too. The other version is similar except involves an entire village and letters

Two that start off as death games but turn into something else: Psyren, Deadman Wonderland

Not a death game but has a similar feel and has a lot of death: Cage of Eden, Bokurano, Cradle of Monsters, Mahou Shoujo Site

Straddles the border of death game and not, definitely not for the faint of heart: Sekai Oni

And

Definitely not a death game but has great psychological elements: Liars Game

Most of those are completed, but not all. I'll admit Cage of Eden got axed (and therefore has a rushed ending) but it's a darn good read most of the way through

Also, if you want to try a visual novel death game, I recommend "Your Turn to Die". You can play it for free atm and is absolutely worth the go.

Check Duds Hunt. It's relatively short, complete, with a decent storyline and a pretty cool ending.