Harry Hooper said:
How does that work? When I follow a link and get to the Globe's access traffic cop, I just move on. Technically, I got to the Globe's site, but I didn't spend any time there.
You don't know it, but you're talking about two different things.
As to your "traffic cop" point, they can see where people drop off on their site. They know how many people are leaving and at what point they're leaving. Google Analytics can track it all well enough, and I'm sure they're probably using other independent analytics as well.
As to the time you spent on the site, first, they can track the average session time per user (and see every users individual session time if they'd like) and bounce rate (someone that goes to a page and leaves before going to any other page on their site). The action you described would drive traffic, which is good for their advertisers, but bad for their own conversion numbers.
More importantly, however, is how well their site is performing relative to previous numbers and to industry standards. At its most basic level, they track the number of people to hit a page with a key CTA ("Call-to-action" like filling out a form on the website) and divide it by the number of people to complete the CTA to get a conversion number.
If you know your own conversion history and industry conversion history, you have some good beginner benchmarks to be able decide the success rate of that event/page. Knowing your budget on that particular event (ghost writers, salaries, website designers, etc) and dividing it by the total revenue created by the event will give you a basic ROI metric to gauge success level.
I have no idea how successful their site is, I haven't paid any attention nor do I care to, but I can guarantee that they have an entire product marketing and digital marketing team that are well aware of their current metrics, past metrics, and future goals.
Edit: As to the Alexa rating, it's good to see traffic increase and your site grow because, in a vacuum, it signifies that you're doing the other important things right. At the end of the day, nobody gives a shit. It's more important to rank well for targeted keywords and phrases. I would bet $100 that the Boston Globe would rather rank #1 in a targeted Google key phrase like "Best United States Newspaper" than have a good Alexa ranking.