Does Stormbringer deal its damage to all units at the battlefield?

Yes, Stormbringer deals damage equal to the chosen friendly unit's Might to all enemy units at the chosen battlefield.

According to the card text: "Choose a friendly unit in your base. Deal damage equal to its Might to all enemy units at a battlefield, then move your unit there."

As noted in the RiftJudge FAQ #3073, you choose both the friendly unit and the battlefield when Stormbringer enters the chain. The damage is dealt to all enemy units present at that chosen battlefield.