You can link to any HTML element that has an
id attribute set, by appending
#id's_value to the end of the page's URL. This, of course, requires two things: 1) the specific point to which you want to link has an element with the
id set; and 2) you search it in the page's source.
This is how a Wikipedia article's Contents links work, for instance, but I don't think it will work on the NY Times articles, since the entire article is made of paragraphs (
<p>) that don't have the
id attribute set.
On the other hand, there are apps like Citebite, that do exactly what you want.
Link directly to quotes in Web pages.
Paste a chunk of text and the URL of the page containing the text and in return get a link that opens directly to your selection and highlights it.