Anonymity is not something you either have or don't have. It's always relative to an anonymity set. Mathematically, a ring signature provides a guarantee of anonymity within the ring.
I'm on the Monero Research Lab team. This article, like most media coverage of academic research, ignores much of the subtlety behind the research. The likelihood that a particular output is positively identified depends heavily on its age relative to our regular protocol upgrades. And it's not like we aren't actively working on ways to improve anonymity. We're in the process of updating the way we choose our fake outputs and discussing best practices for handling very old outputs. I always appreciate research into ways to improve Monero, but I don't think this article does the research justice.