A series of museum exhibits endorsing the other view prompted Raphael Golb to push the online campaign against what he has called "propagandists for a faith-based theory."
The court upheld 19 charges, but it dismissed 10 other counts: aggravated harassment, unauthorized computer use, criminal impersonation and identity theft, the sole felony.
Judges Robert Smith, Victoria Graffeo, Susan Read, Eugene Pigott Jr. and Jenny Rivera agreed with Abdus-Salaam.
Golb was originally sentenced to six months in jail and five years on probation. He remained free on bail during appeals. With the felony conviction thrown out, he will need to be resentenced.
Defense attorney Ronald Kuby said the New York court resurrected criminal libel, "a major federal constitutional issue" that should go to the U.S. Supreme Court. He said they'll decide whether to appeal after the resentencing.
The Manhattan district attorney's office, which prosecuted Golb, declined to comment Tuesday.