An actual paywall would be a lot less likely to work, because when people get to a paywall, they can't see what they're supposed to be buying, so they just go away and never come back. By contrast, this "works" because it gives people what they want unconditionally and then having accepted it without paying, guilts them into making a donation. Nonprofits have been running on this model forever.
But the real question is whether it's actually "working" -- the conversion rate to paid subscribers is evidently around 2%. That's pretty bad. And then they call it a success because it makes up 50% of their revenue instead of 20% as was traditionally true, but is that because subscriptions are up or because print advertising has been falling for so long? They only quote the most recent rate of change rather than the long-term numbers, and there may be one of these going on: [http://xkcd.com/605/]. When you first open a new revenue model, you can pretty well expect the first couple of years to have a higher growth rate than the ensuing years. Once everyone is subscribed who wants to subscribe, you have a hard time achieving any more subscription growth. And if subscriptions stop growing faster than advertising is falling, they're right back into the death spiral of cutting costs to save money which reduces readership which loses revenue which induces cost cutting.