"Having made plain these fundamental truths concerning the Creator, the apostles told the Lystrians of the Son of God, who came from heaven to our world because He loved the children of men. They spoke of His life and ministry, His rejection by those He came to save, His trial and crucifixion, His resurrection, and His ascension to heaven, there to act as man's advocate. Thus, in the Spirit and power of God, Paul and Barnabas preached the gospel in Lystra. AA 180.3"
"For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life."
The EGW passage summarizes the gospel message preached by the apostles, which includes the key elements of John 3:16: God's love, the gift of His Son, and the offer of salvation. While not a direct quote, the EGW passage clearly echoes the core message of John 3:16.