As far as I know, Like buttons are partially served by Facebook, which then knows I've accessed the site (the NYT in your example). This happens even if I do not click the button, do not hover over it, and do not have a Facebook account.
Yes, the default configuration has your page include javascript from facebook.net which the browser will request on every page view
https://developers.facebook.com/docs/plugins/like-button
In the case of this the theguardian.com page it looks like they've got a webbug as the last element of the body, which results in a request to https://www.facebook.com/tr?
Having facebook count views of your like button is probably considered a feature to publishers.