not feasible.
Civilian GPS accuracy sucks, (intentional to prevent US enemies from using GPS guided munitions) so your drone has to use LIDAR or similar navigation methods. Also, in the news story, the drone is only used inside the restaurant, essentially replacing a waiter.
completely feasible (technologically).Technologically, it is fairly easy to set up an autonomous drone and has been for a couple of decades. Think of a Neato or Roomba vacuum cleaner as a starting point. Think of a good AI in a modern game - the pseudo-code is "just" a PAGE table (percepts, actions, goals and environment descriptors). Real-world complications include politics, flight issues, hardware costs and um, that's about it (assuming ethics of such matters died with Asimov). Politics is the big one, as voters might get upset if a few drone oopsies happened to their loved ones. If you don't insist that your drone fly - if you're content with one that rolls, walks, hops or crawls then politics is about the only pragmatic deterrent, and even that boils down to error tolerance in the "goals" part of the PAGE table. Is it OK if your drone spends its life sidling up to anything warm to say "hello" or do you want it to decide to do something more specific? Is it OK if it jay-walks? Do you mind if it inadvertently pushes somebody's baby stroller out into a busy street as it delivers food?... Mere implementation detail (as we used to say about anything challenging).
As for the GPS issue, one obvious implementation is to use GPS up to about 10-20 meters then switch to something like IR, much the way a contemporary car offers GPS for "the trip" but IR for the parking sensors.
Easy stuff, technologically. Too expensive and error-prone for restaurants at the moment, and too politically hot for governments, so far.
If you like the idea of sandboxing this kind of thing, try MIT's (free) StarLogo.
