"In Sodom there was mirth and revelry, feasting and drunkenness. The vilest and most brutal passions were unrestrained. The people openly defied God and His law and delighted in deeds of violence. Though they had before them the example of the antediluvian world, and knew how the wrath of God had been manifested in their destruction, yet they followed the same course of wickedness. PP 157.1"
"But the men of Sodom were wicked and sinners before the Lord exceedingly."
The EGW passage directly expands upon the wickedness mentioned in Genesis 13:13, providing specific examples of that wickedness. It's more than a thematic parallel; it's a direct elaboration.
At the time of Lot's removal to Sodom, corruption had not become universal, and God in His mercy permitted rays of light to shine amid the moral darkness. When Abraham rescued the captives from the Elamites, the attention of the people was called to the true faith. Abraham was not a stranger to the people of Sodom, and his worship of the unseen God had been a matter of ridicule among them; but his victory over greatly superior forces, and his magnanimous disposition of the prisoners and spoil, excited wonder and admiration. While his skill and valor were extolled, none could avoid the conviction that a divine power had made him conqueror. And his noble and unselfish spirit, so foreign to the self-seeking inhabitants of Sodom, was another evidence of the superiority of the religion which he had honored by his courage and fidelity. PP 157.2 Melchizedek, in bestowing the benediction upon Abraham, had acknowledged Jehovah as the source of his strength and the author of the victory: “Blesse…
"Let your light so shine before men, that they may see your good works, and glorify your Father which is in heaven."
Both passages discuss the idea of being a light to others through good works and actions. The EGW passage describes how Abraham's actions influenced the people of Sodom, while Matthew 5:16 is a general principle about letting your light shine.