I'm pretty sure the Times implementation of WinerLinks doesn't have the all-important feature of allowing the author to insert, delete or move paragraphs without breaking external links.
This is just a guess, but I am inferring it based on: 1. The paragraphs have numbers like p1, p2, p3 etc. There's no evidence of reorganization, which would look like this: p12, p3, p4, p9. In other words, there would be no relation between the visual order of paragraphs and the permalinks. 2. They use WordPress, and its model can't support invariant paragraph IDs, because you're editing HTML source, not structures of paragraphs.
My content system can do it because I use an outliner to edit my blog posts. Screen shot.
Each paragraph is a separate entity. It gets a unique ID when it's created, when I press the Return key while typing. That ID does not depend on where it is in the outline. I can reorganize as much as I want and the paragraph IDs won't change. The permalinks stay the same no matter where the paragraph has been moved to.
There are outliners that work in a browser, so you don't need to use an external tool, it could be embedded in your browser-based blogging environment. But to make this work, WordPress itself will have to advance, I don't think you can do this in plug-ins (could easily be wrong). No matter what they will have to store two bits of text for every post: 1. The "source code" which contains the paragraph-level metadata. 2. The HTML rendering. I hope the source code is OPML, and they permit external editors like mine to be used to edit the posts. I asked Matt for a feature that would allow a bit of XML text to be stored in WordPress alongside the HTML. I don't think he understood the application at the time. This is the application (and there will be others as well, separating source from rendering is basically a good way to gain leverage).
BTW, here's the source code for this post. I store it in my CMS alongside the HTML rendering. If you change the extension from .html to .opml you'll get the source.