A lot of those steps in that diagram are outside of the actual Workflow of a Workflow Schema. The schema kicks in when the asset goes from Under Construction or Safe Edit in to apply for approval. So Under Construction and Safe Edit are actually not "Workflow Schema" steps per se.
The only time the asset is actually in "Workflow" is in the pending approval status. That's when the steps and conditions kick in as that's where the approval process happens.
The people who are approvers of a particular workflow step (part of the step condition) are the ones that can approve or reject.