I don't think it does. That command was given in a particular pre-death, pre-resurrection, pre-pentecost missionary situation. (In another place Jesus describes Himself as sent only to the lost sheep of the house of Israel.) The ministry to the Gentiles is a post-pentecost deal.
It's interesting to try to make that pre missionary journey instruction stay in force after Pentecost, but then we'd have to re-think Paul's missionary journey.
That reminds me: there were Jews in Rome, so even if the command DID apply, Peter's going to Rome would not necesarily be a violation of it, right?
Anyway, we're let with some evidence that Peter went to Rome and no evidence (so far) that he didn't. The preponderance, therefore, is that he did.
Well....he "does" say [Matthew 10:5] "These twelve Jesus sent"/ Douay Rheims.
Paul was selected as the Gentile's Apostle while the "Twelve" still had their mission....post Pentecost. Don't you agree?
Read the entire thread and you will find that there is no evidence that the real Peter was there in Rome --- just an impostor calling himself "Peter" whose real name was Simon Magus, the first Bishop of the counterfeit Church of Rome.