Yes, of course it is correct, but the English here is too ambiguous to capture the precise nuances of the verb tenses of "belief" and "condemn." A more informative translation is as follows:
"The one persistently committing trust unto Him is not being judged. But the one not persistently committing trust already has been permanently judged because he has not permanently committed trust unto the name of The Only Begotten Son of The God" (The Gospels: A Precise Translation).
Christ did not come into the world to condemn the world, because it and the people within it--every one--had already been pronounced guilty unto death by The Righteous God, based on the sin of Adam (of whom every one bears his genetic substance).
But the love gift of God, the Person Jehovah (YHWH), invested a perfect sinless human body by standing in for us/me so as to receive our/my punishment--a piercing, burning mutilation and shameful reputation, paying the blood-price from his own veins; so that we/I might be judicially pronounced guiltless and free IF I would simply accept this release from condemnation as an undeserved but compassionate benefit of offered friendship.
Amen!
"Be not afraid, only believe." (Mark 5:36)