When I worked at a convenience store a "distributer" came in weekly, took inventory, and delivered tobacco products.So according to Mr eliquid, (@ 6:10) they themselves believe that USPS will not do commercial shipments, but also have no idea if UPS and FedEx will even take commercial shipments, so they may not be able to get any inventory.
However, to the best of my knowledge, UPS and FedEx do deliver cigarettes, snuff and chew to stores, so why would they not deliver vape supplies when they are all the same product - "tobacco products"? I doubt a small, independent convenience store gets all of it's tobacco products via LTL carriers. At least some of it probably gets delivered by UPS/FedEx. But I never worked at one so I can't say for sure.
Not sure how it's done today. It was 51 years ago when I worked at a convenience store.