The Greek word pro·sky·ne′o, is found in the Bible around 60 times. According to Unger’s Bible Dictionary, it literally means to ‘kiss the hand of someone in token of reverence or to do homage.’ An Expository Dictionary of New Testament Words, by W. E. Vine, says that this word “denotes an act of reverence, whether paid to man . . . or to God.” In Bible times pro·sky·ne′o often included literally bowing down before someone of high stature. So, pros·ky·ne′o is properly rendered “do obeisance” at times, because often in the Greek Septuagint Version of the Bible the action of this verb is directed to men; for example, where the patriarch Abraham bowed down (pros·ky·ne′o) to the pagan natives of Canaanland, the Hittites, the sons of Heth. (Gen. 23:7, 12) Or, as when the patriarch Jacob and his wives and his children all bowed down repeatedly (pros·ky·ne′o) to his twin-brother Esau, whom God said He hated. (Gen. 33:3, 6, 7)
Clearly, the word pro·sky·ne′o, rendered “worship” in some Bible translations, is not reserved exclusively for the type of adoration due God. It can also refer to the respect and honor shown to another person. In order to avoid any misunderstanding, some Bible translations render the word pro·sky·ne′o as “pay him homage” (New Jerusalem Bible), “honour him” (The Complete Bible in Modern English), “bow down before him” (Twentieth Century New Testament), or “do obeisance to him” (New World Translation).
I hope this helps in your understanding of why pro·sky·ne′o is translated the way it is in the NWT because Jesus certainly occupies a pivotal role in true worship, one worthy of honor and respect. He is the only way through which we are able to approach God. Jesus is worthy of our honor, respect, and obedience.