The body of the article says they picked the car up from a Tesla service center (which is accurate--you can order your car from a showroom, but you pick it up at the service center). The only reference to a "dealership" is in the photo caption, which was likely written by someone else who wasn't as familiar with Tesla.

They don't. Tesla has stores that are company owned. Dealerships are a franchise system from what I understand.

Of course Tesla has dealerships. They just operate their own, rather than relying on third parties.

Not all Teslas are ordered online.

They do. We have one in Columbus, Ohio.