> It seems strange that this article does not actually embed the tweets mentioned

That's because a tweet can be deleted by the owner of the tweet, and the embed won't show it in the article anymore. Embedding tweets in an article is usually bad practice, and it also slows down the page with unnecessary Javascript.

Frankly I see nothing wrong with just copying and pasting a Tweet, so now you have a verbatim copy of what was said. Then there is the issue of edited tweets which apparently are coming soon, giving another troll tool to users of Twitter.