"The Remedy Looking upon man, God saw his desperate rebellion, and He devised a remedy. Christ was His gift to the world for man's reconcilement. The Son of God was appointed to come to this earth to take humanity and by His own example to be a great educating power among men. His experience in man's behalf was to enable men to resist Satan's power. He came to mold character and to give mental power, to shed abroad the beams of true education, that the true aim of life might not be lost sight of. The sons of men had had a practical knowledge of evil; Christ came to the world to show them that He had planted for them the tree of life, the leaves of which are for the healing of the nations. CT 33"
"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."
Both passages highlight God's love for humanity and the gift of Jesus Christ for salvation. While the EGW passage expands on the purpose of Christ's coming, it clearly echoes the core message of John 3:16. The connection is strong, but 'thematic_parallel' is a better fit than 'explicit_allusion' as it's not a direct quote.
"Under God, Adam was to stand at the head of the earthly family, to maintain the principles of the heavenly family. This would have brought peace and happiness. But the law that none “liveth to himself” ( Romans 14:7 ), Satan was determined to oppose. He desired to live for self. He sought to make himself a center of influence. It was this that had incited rebellion in heaven, and it was man's acceptance of this principle that brought sin on earth. When Adam sinned, man broke away from the heaven-ordained center. A demon became the central power in the world. Where God's throne should have been, Satan placed his throne. The world laid its homage, as a willing offering, at the feet of the enemy. CT 33.1"
"For none of us liveth to himself, and no man dieth to himself."
Ellen White directly references Romans 14:7 in this passage.