He didn't preach to them. And where it does mention preaching, it doesn't say that he did so to unbeliever.
FreeGrace2 has already pointed out that Paul wanted to preach to unbelievers:
Romans 15:20
It has always been my ambition to preach the gospel where Christ was not known, so that I would not be building on someone else’s foundation.
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http://www.christianforums.com/t7787859-5/#post64503468)
That you persist in asserting that Paul never preached the gospel to unbelievers is baffling. However, I shall oblige. Examples include Philip (and that of various Christians), Peter, John, and Paul). All scriptures are from Acts.
Chapter 8, verses 4 & 5
Those who had been scattered preached the word wherever they went. Philip went down to a city in Samaria and proclaimed the Messiah there.
Did they only encounter believers? Obviously not.
Ibid., verses 9-13
Now for some time a man named Simon had practiced sorcery in the city (of Samaria) and amazed all the people of Samaria. He boasted that he was someone great, and all the people, both high and low, gave him their attention and exclaimed, “This man is rightly called the Great Power of God.” They followed him because he had amazed them for a long time with his sorcery. But when they believed Philip as he proclaimed the good news of the kingdom of God and the name of Jesus Christ, they were baptized, both men and women. Simon himself believed and was baptized. And he followed Philip everywhere, astonished by the great signs and miracles he saw.
Ibid., v. 25
After they had further proclaimed the word of the Lord and testified about Jesus, Peter and John returned to Jerusalem, preaching the gospel in many Samaritan villages.
Ibid., v. 40
Philip, however, appeared at Azotus and traveled about, preaching the gospel in all the towns until he reached Caesarea.
Chapter 10:42
He commanded us to preach to the people and to testify that he is the one whom God appointed as judge of the living and the dead.
Peter confirms that what he preached was to all and sundry, for Jesus had told him to do so to 'all the people'.
Chapter 11, vv. 19-21
Now those who had been scattered by the persecution that broke out when Stephen was killed traveled as far as Phoenicia, Cyprus and Antioch, spreading the word only among Jews. Some of them, however, men from Cyprus and Cyrene, went to Antioch and began to speak to Greeks also, telling them the good news about the Lord Jesus. The Lord’s hand was with them, and a great number of people believed and turned to the Lord.
Ch.13:2-5
While they were worshiping the Lord and fasting, the Holy Spirit said, “Set apart for me Barnabas and Saul for the work to which I have called them.” So after they had fasted and prayed, they placed their hands on them and sent them off. The two of them, sent on their way by the Holy Spirit, went down to Seleucia and sailed from there to Cyprus. When they arrived at Salamis, they proclaimed the word of God in the Jewish synagogues. John was with them as their helper.
Ibid., v.32 (Saul to the synagogue at Pisidian Antioch)
“We tell you the good news: What God promised our ancestors
Ch.14:1-7
At Iconium Paul and Barnabas went as usual into the Jewish synagogue. There they spoke so effectively that a great number of Jews and Greeks believed. But the Jews who refused to believe stirred up the other Gentiles and poisoned their minds against the brothers. So Paul and Barnabas spent considerable time there, speaking boldly for the Lord, who confirmed the message of his grace by enabling them to perform signs and wonders. The people of the city were divided; some sided with the Jews, others with the apostles. There was a plot afoot among both Gentiles and Jews, together with their leaders, to mistreat them and stone them. But they found out about it and fled to the Lycaonian cities of Lystra and Derbe and to the surrounding country, where they continued to preach the gospel.
A great number believed, but not all. It says in verse 7 that they continued to preach the gospel.
Ch.15:7 (The Council of Jerusalem)
After much discussion, Peter got up and addressed them: “Brothers, you know that some time ago God made a choice among you that the Gentiles might hear from my lips the message of the gospel and believe.
Ibid., v.36
Some time later Paul said to Barnabas, “Let us go back and visit the believers in all the towns where we preached the word of the Lord and see how they are doing.”
When Paul ministered to believers, he specifies that that is indeed the case.
Now, do you accept that Paul (and others) preached the gospel to unbelievers?
This is all irrelevant, though. You still haven't shown that unbelievers were his audience in relation to chapter 15.
Paul questions the integrity of the Corinthian believers and points out that there is sexual perversion (incest), irreverence of the Lord's Supper, and a denial of the resurrection of the dead among them. His recapitulation of the gospel is entirely consistent with such concerns. Paul directly addresses those that may not be true believers:
1Now, brothers and sisters, I want to remind you of the gospel I preached to you, which you received and on which you have taken your stand. 2By this gospel you are saved, if you hold firmly to the word I preached to you. Otherwise, you have believed in vain.
So, sure, Paul accounted for unbelievers in his letter. He speaks directly to them. It is they that would most benefit from a restatement of the gospel.
Your problem is that Paul says in his letter that the gospel he preaches (v.11 '...we preach...') is the gospel '...you believed'. You have already said that there is only one gospel and that it is not modified. You were then forced to say that Paul did not preach this gospel to unbelievers because it would mean that unbelievers would be included in those whose sins Jesus died for. But, clearly, Paul did preach this gospel to unbelievers.
