Interpreting is what you are doing and putting the spin on it that fits your world view. When God says something he means it like when Jesus said "I am the way the truth and the life, no man comes to to the Father but by Me." Many people call that a narrow interpretation too but if you are truly a Christian you know it to be true.
It is disturbing truth to many who hold secular humanistic views and think that Buddhism, Taoism and the Hindu faith lead to God too. But Jesus said in Matthew 7:13-14 "Enter by the narrow gate; for the gate is wide and the way is easy, that leads to destruction, and those who enter by it are many. For the gate is narrow and the way is hard, that leads to life, and those who find it are few."
That passage from Genesis does not need to be interpreted it is being stated. When God was talking to Noah; He was talking about all encompassing judgement nothing more, nothing less. God says a lot with little and there is substance and power in what He says.
I don't read it as only applying to all encompassing judgment. And no, I am not a humanist, I beleive Jesus is the way, the truth and the light