Is it normal for Snapshot Replication job to be constantly running?
This is correct state of Distributor Agent. After delivering from snapshot (which was created at scheduled time by Snapshot Agent) it triggered action that has finished as "Delivered Snapshot from the (...)". Delivery is performed by a Distributor, which is always on, and looking for new actions (Snapshots).
So in reality there are two jobs for Snapshot replication: Snapshot Agent triggered by schedule and Distributor Agent waiting (active) for any new actions. "No replicated transactions are available" means here, that there are no new snapshots to distribute.

By design Distributor Agent needs to run constantly and listen for new snapshots which are scheduled in Snapshot Agent.