Paul is arguing that “it is not the hearers of the law who are righteous before God, but the doers of the law who will be declared righteous” (v 13). Everyone agrees that the following two verses are an illustration of this truth, and the declaration of righteousness picks up at v 16 where Paul concludes that this will happen “on the day when God judges the secrets of everyone according to my gospel through Christ Jesus.” This is why the NIV puts vv 14-15 in parentheses. So far no problem.
But what to do with vv 14-15? The problem partially is due to an ambiguity in the Greek word order with φύσει. Word for word the Greek reads, “for when Gentiles (ὅταν γὰρ ἔθνη ) the not law having (τὰ μὴ νόμον ἔχοντα) by nature (φύσει) the things of the law do (τὰ τοῦ νόμου ποιῶσιν).
If you take φύσει with the preceding, Paul is thinking of Gentiles who are born apart from the (Mosaic) law; nevertheless, they obey the law and hence they must be Christian Gentiles (so Cranfield).
If you take φύσει with the following, Paul is describing Gentiles who naturally keep the law. This, of course, could not be the Mosaic law, but would be the natural sense of right and wrong that God has embedded into the conscience of people generally (so Moo).