Nonsense. There is nothing at all to suggest "it was already there." It does say that Linus was the FIRST to obtain the episcopate and that event happened after the death of Peter and Paul. Nothing in the passage comes close to suggesting Peter was the first Bishop of Rome which would certainly have been pointed out if true. None of Peter's epistles say a thing about Peter being a Bishop of Rome, nor does Paul's letter to the well established Chucrch in Rome. It is a purely made up fiction.
No, the passage itself shows Linus was the first bishop AFTER Peter’s martyrdom. He was the first to OBTAIN the EPISCOPATE. That’s an office. A specific office that already existed. And his obtaining it was only possible when Peter was martyred.