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You can stream Bokurano (2007) on Crunchyroll with a subscription.

During a summer camp, 15 children, 8 males and 7 females, find a grotto by the sea. Deep within they discover working computers and some electronic equipment, and later the owner, a man called Kokopelli. Kokopelli claimed to be a programmer working on a brand new game, in which a large robot has to defend the Earth against fifteen alien invasions. He persuades the children to test the game and sign a contract. All but one of them signs; barely a moment later they mysteriously awaken on the shore believing what happened was just a dream.

Bokurano is a show that explores themes of mecha, anime, psychological. It also touches on death game.

Trailer