The split computing approach, where the head and tail models are respectively distributed between the IoT device and cloud, suffers from high network latency especially when the cloud is located far from the IoT device. To mitigate this problem, we introduce a distributed split computing system (DSCS) where an IoT device (called split computing requester) broadcasts a split computing request to its neighboring IoT devices. After receiving the request, the neighboring IoT devices (i.e., requestees) distributively determine whether or not to accept the split computing request by taking into account the unnecessary energy consumption and computation time. To minimize energy consumption while maintaining a specified probability of on-time computing completion, we develop a constrained stochastic game model. Then, a best-response dynamics-based algorithm is used to obtain the Nash equilibrium. The evaluation results demonstrate that the DSCS consumes can reduce more than 20% energy consumption compared to a probabilistic-based acceptance scheme, where the IoT devices accept a split computing request based on a predefined probability, while providing high on-time computing completion probability.