Again, its the title same title argument everyone makes. Read the 2nd to last bullet. It only specifies they were rivals, not who won. When you read other confirmed points in the story, Mihawk stopped fighting Shanks because he lost his arm (explained when Luffy got his 30 million bounty), not because when won. On the flipside, there is no indication that Shanks lost power either, considering what Oda has shown us.
Its not about whether or not Mihawk is the better swordsman, its about how the story presents the duo, and at this time the duo has never been presented as anything other than equal in this regard when it comes to their duals.
Also, nothing here insinuates Shanks even vies for the WSS title. Hes a Yonko with clearly different goals and a different mindset, clearly.
I'm curious what people think Mihawk is going to do next. He doesn't have his Shichibukai title anymore and his only notable relationship is with Shanks. With the coming war, he has to be a part of some combative front. And its very possible that is going to be with Shanks as an equal partner. There are heavy indications that Luffy and Shanks will fight (and may even be the final battle depending on the observer), tying Mihawk to a certain group for Zoro helps in this case, as Blackbeard has Shiryu, Im has the Monk Gorosei with Shodai and Akainu has Fujitora.
Mihawk being associated/allied with the Red Haired Pirates gives him a lasting purpose to the EoS for Zoro. I'm not sure why people don't see that as a possibility.