"“And the devil, taking Him up into an high mountain, showed unto Him all the kingdoms of the world in a moment of time. And the devil said unto Him, All this power will I give Thee, and the glory of them: for that is delivered unto me; and to whomsoever I will I give it. If Thou therefore wilt worship me, all shall be Thine. And Jesus answered and said unto him, Get thee behind Me, Satan: for it is written, Thou shalt worship the Lord thy God, and Him only shalt thou serve.” EW 157.1"
"Again, the devil taketh him up into an exceeding high mountain, and sheweth him all the kingdoms of the world, and the glory of them;"
EGW is retelling the temptation of Christ, and the details are very similar to Matthew 4:8. It is more than a thematic parallel.
"Satan presented before Jesus the kingdoms of the world in the most attractive light. If Jesus would there worship him, he offered to relinquish his claims to the possessions of earth. If the plan of salvation should be carried out, and Jesus should die to redeem man, Satan knew that his own power must be limited and finally taken away, and that he would be destroyed. Therefore it was his studied plan to prevent, if possible, the completion of the great work which had been commenced by the Son of God. If the plan of man's redemption should fail, Satan would retain the kingdom which he then claimed. And if he should succeed, he flattered himself that he would reign in opposition to the God of heaven. EW 157.2"
"Now is the judgment of this world: now shall the prince of this world be cast out."
The EGW passage describes Satan's attempt to retain control of the world, while the John verse speaks of Satan being cast out. There's a thematic connection regarding Satan's dominion, but it's not a direct allusion or principle.