The cited verses do not address all mankind, but only Israel.
Genesis 1:27-31a tells us why God created us and what he expects of us. Under him (which means trusting in him and loving him), we are to inhabit the world and be the caretakers of God’s creation. Even in our fallen state, we are still to do this. How we do what God created us to do (in our fallen state) God relayed to us in the Ten Commandments.
Along with believing the Creeds, and of course living in Christ, we are to follow the precepts of the Church. If you mean: Do we have a greater obligation than our non-Catholic brethren? I think we do because “to whom much is given much is required.”
I assume you mean non-Catholic Christians, yes? CCC #817-819 may be helpful.
Non-Christians CCC #846-848.