No, that is esthio.
a different word trogo which does mean, as wide awake stated, to literally gnaw
That is an even more intense word, which continues the aggressiveness of the language used in the passage, starting in 6:54 - to rip with the teeth.
John 6:53, however, doesn't use either trogo nor phago esthio, just esthio.
Again, I have to disagree.
What Greek bible site or version are you looking at? Here is my source for word by word translations.
http://www.greekbible.com/index.php