Certainly the Lord used Peter's God-given affirmation of Jesus as "the Messiah, the Son of the living God" to instruct His disciples about the foundation of His Church.
You RCCers believe that the Lord was founding His Church on Peter, and this is the fundamental underpinning of papal authority (that's why this interpretation is so important to you).
Me, I believe that Jesus is referring to Peter's God-inspired statement of faith. [One only needs to read a couple of verses later to see Jesus referring to Peter as "Satan". It's hard to believe that Jesus is bi-polar.]
Your position that anyone who does not accept the RCC interpretation is not a Christian is certainly not uncommon in the RCC. In my youth, and long before God enlightened me, we were taught to pity the poor Protestants who were all going straight to hell. [Unlike us RCCers who, at least, had a pretty good shot at Purgatory]
Thank God for His Word!