What do you think is Gabriel’s purpose in the play?

The character of Gabriel is analogous to that of the wise fool in Shakespeare's plays, providing a kind of commentary on events and other characters in the play. Gabriel's disabilities, stemming from his cognitive impairment caused by a war injury, cause him to engage in rambling speeches about his relationship to the angels. In the Bible, when the angel Gabriel blows his trumpet, he's indicating the return of the Lord to earth. This is a common trope used in gospel songs. And in Fences, Gabriel sees himself in the role of his namesake, telling us how he's waiting for St. Peter to call upon him to open the gates of heaven.
Troy exploits Gabriel, but his disabled brother is unable to comprehend this. However, in the guise of the angel, Gabriel warns of judgement day and says that Troy's name is in St. Peter's book. Despite his chronic disability, Gabriel is still able to provide the audience with a wise commentary on his brother's unacceptable behavior, which points ominously towards the fate of his soul.