How could Gentiles glorify God for His mercy?

Gentiles could glorify God for His mercy because the promises made to Abraham, Isaac, and Jacob extended to them, so that through those promises Gentiles might glorify God for His mercy. This mercy and grace of God is the basis, even as Israel's rejection opened the way for Paul's ministry to the Gentiles.

Les explains that God's promises to the fathers—Abraham, Isaac, and Jacob—were the seed of Gentile inclusion. Israel was first the minister to the Jews, but after their crescendo of rejection, culminating in stoning Stephen, Paul turned to the Gentiles. Yet the verse states that even through those promises, Gentiles might glorify God for His mercy. Les says he now understands this mercy and grace of God as he should have.

Romans 15:9

And that the Gentiles might glorify God for his mercy; as it is written, For this cause I will confess to thee among the Gentiles, and sing unto thy name.

How are the Gentiles included through the promises made to Abraham, Isaac, and Jacob?

Gentiles are included through the promises made to Abraham, Isaac, and Jacob because God's mercy and grace extend those covenants beyond Israel to the Gentiles, so that Gentiles might glorify God for His mercy. This inclusion was seeded in the Old Testament and realized when Paul goes to the Gentiles after Israel's rejection.