I don't think I've ever been in a movie theater other than restaurant/theater hybrids (where tables have specific waiters) where this was done. But either way, the author says he was working the bar (which sounds more like a bar/concession stand hybrid), not serving tables.
The Alamo Drafthouse chain of theaters, of which there is at least one in Austin and one in the DC suburbs, has table service. And, if I remember correctly, the bar is set-up like a normal pub bar (and separate from non-alcohol concessions). So, you can order a drink in advance of seating, as you would at a a pub (where you'd normally tip the bartender) and you can order drinks at your seat.
It is a bit strange/confusing that the author didn't clarify, as very few theaters serve alcohol at all. And most that do don't have a stand-alone bar or table service, just beers at the concession counter.