That alone could potentially have far reaching consequences. I agree that the article is a bit light on details though.
How did Science get Scihub's server logs? Did scihub give them to Science? It's annoying that the economist is not linking to this supposed Science 2016 publication. If they did, I would have known how to access and read that publication (because I know this one website which would let me read it).
The Economist's usual readership is literate and can use search engines. The Science publication is literally the first result of the obvious search term.
If the Economist is in the business of distributing information, linking to a journal should sort of be one of the things they do. Even Buzzfeed and such outlets now do the common courtesy of linking to papers that they are talking about.
And I would daresay that one should probably not trust logs when going through Tor.