I did some research on this subject about 2 years ago. While the translation of the verse is nominally correct in the New World Translation, the way that the Governing Body has Witnesses understanding the terms within does not seem to go further than what one gathers at first blush.
While the basic thought of not being too wordy or saying phrases over and over again are correct, this instruction is in reference to praying “just as the people of the nations do.” Who are these people and how did they pray? That would be necessary to know if Christians were to avoid imitating them.
If one translates this texts with words more common in our language, especially from a Jewish vocabulary (and it would still be accurate), notice what happens: “Don’t babble in prayers like the Goyim (Gentiles) do. They think that by saying many words that they’ll be heard.”
The word rendered “babble” literally means “flood of empty words.” It doesn’t really mean the same words over and over again, as Therevealer pointed out from Mark 14:32-39. This would mean one could not sing the Psalms to God or other religious songs like modern hymns (or even the Witnesses’ “Kingdom songs”) because various verses have antiphons or choruses that repeat themselves over and over again. (Compare Psalm 136.) The use of a lot of words is also not of itself wrong because that would leave out things like Psalm 119.
Babbling in prayer like the Gentiles was more likely in reference to the practice of reciting incantation-like petitions. These went on and on, usually with a list of various deity names. The belief was that such long, repetitive prayers would wear down the gods and force them into giving what the petitioner wanted. This shows what type of personality the pagans believed their gods possessed, that they were difficult to get to and hard to convince and far from being generous.
Jesus instruction was not about merely praying with the same words again and again, even if they were already written down and composed like one of the Psalms. He even talked about repeatedly petitioning God about the same thing like the woman who wore down a judge with her petitions.—Luke 18:1-8.
Rather it appears that Jesus was instructing his followers not to think of their God as being as inconsiderate or with as much disinterest or lacking deference as the pagan gods were considered to be. YHWH did not need to be approached by using a list of his name and all his titles to get his attention. One did not have to wear him down with many words in order to be heard. In fact, God “hears” before the petitioner can even ask, Jesus said.
I offer the possibility that this was likely less regarding instruction of what type of prayer to use and more an instruction on how Christians were to view the God that they were praying to. Jesus said that his followers need not be like these worshippers of false gods because Christians worshipped their “Father” who “knows what you need before you ask.”—Matthew 6:8.
This view is comparable to what most in mainstream theology teach. Should it prove more accurate than the one the Watchtower teaches, this could be another reason they should not condemn the prayer practices of other faiths as they do. It also shows that—as usual—they are more concerned with the mechanics of prayer then they are of the One to whom they offer prayer.