I enjoyed reading the article, but there's a pretty good chance this is PR for Scoot

The only advantage I could think of is that he could be out and about, have an order come through and pick up a scooter to make the delivery. Rather than be tied to wherever his personal scooter is.

There's convenience, but maybe also the moped rental subscription turns out to be cheaper (or similar but more predictable) than the costs of fuel, licensing and maintenance on your own scooter.

Well, I'd assume it's faster than using a a bike and cheaper than using a car or his own moped. I wonder if he's not saying that he's hacking the system by signing out a moped when he's going from restaurant -> customer or customer -> restaurant and then signing it in again when he's waiting for a pickup or making a delivery.

Same here - I can see how it might be cheaper than running a non-electric moped, and thus increase his weekly takings.

Maybe other delivery drivers are using cars and thus get stuck in traffic more? Not sure how feasible/likely that is in SF though (UK here)