What does “Awesome” mean when you are complimented by an Apple-shop salesclerk on your answer to a barrage of his questions?

I think the key to understanding that phrase you quoted is another quote from the article:

In other developments, available phone numbers ran out, forcing the introduction of unpleasant new area codes. “Awesome” went from being a risible word used only by stoners and surfers to an acceptably ubiquitous modifier, the Starbucks of adjectives.

Twenty years ago, someone saying: "Awesome!" (or also commonly: "Totally awesome, dude!") was, as the author says, something from the surfer/stoner subculture. It would not get much mileage in mainstream use.

Nowadays, particularly among the younger generation, it is very commonly used. You can substitute "Great!" or "Excellent!" and get the same meaning.

However, as the other answers suggest, it can also be used disingenuously, as in "Oh, that's nice." That's why the author feels the need to clarify "And I think he meant it..." to show that the clerk was really saying it was great.

What was the clerk saying was great? It could be open to interpretation. Given that the author uses that line to close the article, which is about moving back to New York, I would say they meant it to refer to the move in general.

It means ‘I’m not the least bit interested in your miserable, boring life, but I have to say this because I’m told to.’

It means they can't think of anything else to say, but are trying to build rapport with you in a half-naive manner in order to potentially get you to buy something. Either that or they are on Adderall.

They don't get commission on it, but their "numbers" look better and they get respect from their peers when they sell stuff.

There is a possibility that when you pause at the end of a sentence, you intend to end the exchange. Since the other party to the "conversation" has a vested interest in causing you to continue (but has nothing substantive to contribute) he needs to utter a short encouraging sound. The Neanderthals probably grunted.

Divergent cultural evolution led to a variety of forms for this utterance (such as uh huh, right, and, wow, brilliant or awesome). As a result of globalisation, these variants are no longer localised and we wonder whether the forms with which we are less familiar may have some meaning that we do not expect in our native dialect.

In fact, they all mean the same thing -- nothing.