I've run 5 (ignoring ultras) thus far and I'm pretty sure my entire cost for those 5 wouldn't be much more than $1600 in total (the bulk of which would be the Fenix 3 watch.)
It includes $578.80 in new clothes (not shoes). That's not entirely unreasonable -- I have a waterproof running jacket that was north of $100, for example. I like my running shorts from Road Runner, which probably cost $50 apiece. And while I amortize those things over several years, it's not unreasonable to think a new running might count that cost for their first (and probably only) marathon.
There's $235.40 for four races -- 5ks and 10ks. That's kind of a pricey for races that short. At least at that price it should come with some nice technical tee shirts, so you don't need to buy them. (I originally trained in cotton, and yeah, the new shirts are better.)
They way they incorporate the $130.50 for the gym is reaching (she already had the membership). I have substantial doubts of the necessity for $210 for massages. The calculation of $95 for travel to those 5ks is bizarre, and $163.46 for post-race celebrations is ridiculous.
So yeah, you can spend $1,600. You can spend a lot more, especially if you travel to a race. You can also spend a lot less.
The article itself is a bit silly, though it's not entirely out of place to say, "Hey, there are things you don't take into account in the cheap sport of running". That's fine.
But it really, really doesn't support the Outside article's claim that endurance running is an expensive sport. In fact it's kinda the opposite: the NYT author lives with her parents and saved a bunch of costs that way.
Fortunately, it's not really important to the Outside article. It's a dumb thing to cite, but it's nonetheless true that a lot of people who do endurance sports have more money, and it has nothing to do with what those sports costs.
(Though hoo boy, you should see the money on display at an Ironman.)