JOEL - Parley P. Pratt's "Mormonism Unveiled: Zion's Watchman Unmasked" was a pamphlet written solely by himself in an emotional response to the many lies and hostile articles written by a Protestant minister named LeRoy Sunderland. Parley's attitude was obviously quite livid throughout the writing of this pamphlet which may at times have allowed his emotions to cloud his judgement about some of the things he said.
However, the "prophesy" he makes correlates to a prophesy that he refers to in the Book of Mormon earlier in the article. He speaks of 3 Nephi Chapter 21:11-21 when he says, "where all who will not hearken to the Book of Mormon, shall be cut off from among the people; and that too, in the day it comes forth to the Gentiles and is rejected by them. And not only does this page set the time for the overthrow of our government and all other Gentile governments on the American continent, but the way and means of this utter destruction are clearly foretold; namely, the remnant of Jacob will go through among the Gentiles and tear them in pieces. like a lion among the flocks of sheep. Their hand shall be lifted up upon their adversaries, and all their enemies shall be cut off. This destruction includes an utter overthrow, and desolation of all our Cities, Forts, and Strong Holds -- an entire annihilation of our race, except such as embrace the Covenant, and are numbered with Israel." (Mormonism Unveiled, Pratt p.15)
These are the things that Jesus predicted will happen to all the people in the latter-days if they harden their hearts and not hearken to the Book of Mormon. At the time Parley made his prophesy, it seemed that that was they way things were going to go. And if the people of his day continued to harass and persecute the saints, he believed that "within five or ten years" everyone would either be converted to the Lord's Church or would be destroyed as predicted by Jesus in the 3 Nephi 21:11-21 scriptures.
But obviously, the governments were not completely overthrown, cities were not desolated, and an entire race was not annihilated. Were both Jesus and Parley wrong? No! Here is the reason why.
Later in 3 Nephi 21 Jesus places a provision on His earlier prophecy when He said:

"But if they will repent and hearken unto my words, and harden not their hearts, I will establish my church among them, and they shall come in unto the covenant and be numbered among this the remnant of Jacob, unto whom I have given this land for their inheritance;" (See 3 Nephi 21:22-29)

Parley's and Jesus' prophesy of destruction did not need to come to pass, because later on there were enough people who did not harden their hearts and who were willing to listen. Because of that God did not destroy them and He was able to establish His church among them.
Therefore, Parley's "prophesy" was essentially valid if opposition and hatred against the Church had continued in the way it seemed to be going at the time he said it. Fortunately that did not happen and Christ was able to firmly establish His Church on the earth as it is today.