No. Jumanji does not kill. The artifact has plenty of opportunities during the game, if its goal was to kill, it certainly could knock off one or both players but it doesn't. The game forces compulsion to play to emulate real life's obligation to continue on despite adversity.
Jumanji appears to be an artifact designed to teach the players important values, as games often do, but with a far more sensory-immersion effect. Considering when the game ends, the lessons learned are lasting moral ones, learned under realistic conditions with examples of the consequences of actions fully displayed. These lessons teach about the consequences of choices, quality of relationships, ethics and expound upon the idea that bad choices made in youth could have long term effects on one's life.
And like the seminal Cat in the Hat, any damage done is reversed by the end of the game. A moral fable with a bit of faux terror to drive home the point.