What is the biblical purpose of the Abrahamic covenant in this teaching?
The Abrahamic covenant was to establish Israel as a nation of people in their geographical land, over which God Himself would one day come and be their King. It was only for the Jew; afterward Israel could go out and evangelize the nations, but not until that fulfillment.
Les explains that the whole purpose, from Genesis onward, was in fulfillment of the Abrahamic covenant: Israel was to be a nation of people established in their geographical area of land, over which God Himself would one day come and be their King. That was only for the Jew. Then Israel could go out and evangelize the nations, but not until. So the Jews were correct in their mentality that they were to have nothing to do with Gentiles. In Acts 10, God had something else in mind and pressed Peter to go with these men to Caesarea; apart from that pressure, Peter would never have gone. Six believing Jews accompanied Peter, making seven, God's perfect number.