Because langauge has changed so can terms we use in the bible, if the idea of a 'sinful nature' is believed to be taught by the bible and the translators put is in there reflecting what they believe the passage is saying, so be it. Every translation you read is laced with translational bias' There isn't any getting around that.
For example in Col 2:17 it has this in these translations:
ESV Colossians 2:17 These are a shadow of the things to come, but the substance belongs to Christ.
NET Colossians 2:17 these are only the shadow of the things to come, but the reality is Christ!
KJV Colossians 2:17 Which are a shadow of things to come; but the body is of Christ.
and I disagree with each of these translations. My translation would read:
ME Colossians 2:17 These are a shadow of things to come, but let the body of Christ.
the KJV adds a verb there and others to me distort the meaning of the passage by putting 'reality' or 'substance', instead of 'body'
This is the only place where the translators stray from how they translated the same phrase in other parts of the bible.
Now with that said, they are still correct in their translation, it can mean the things they say it does, I just disagree with them because of my theology as opposed to theirs, and this will happen in all translations.
Now, I would have to see where the NIV translates 'sarx' as world in their text to see why they did it. I didn't see it translated as that in the text when I did a quick scan of it. My guess without reading the text is because it may mean 'people' of the world, not the 'earth'
Chris