Members of the group said that Prince Pierre and his entourage "were being completely obnoxious".
"The next thing I saw, all hell broke loose,'' one witness told the New York Post.
Friends of the prince claim that Hock started the fight, however. One said: "The prince walked up to the table, and Adam just slammed him for no reason.
"Stavros jumped in to help Pierre, and then he got slammed in the face."
Hock is alleged to have sent the prince sprawling, before going on to punch out Mr Niarchos, 26, and the other two men - Vladimir Restoin Roitfeld, 27, a French art dealer, and their friend Diego Marroquin, 33.
The witness said that Prince Pierre: "...fell very badly. He flew across the room and landed on a table on the other side.
"Pierre's face looked broken, with deep cuts and blood everywhere. He looked like he needed plastic surgery."
The prince was treated at the New York Presbyterian/Weill Cornell Medical Centre following the incident on Saturday night, before being released.
Hock, 47, was arrested and appeared at Manhattan Criminal Court.
He told the court: "I was defending myself and others... Why aren't [the prince and his entourage] handcuffed?"
He was released to appear back in court next month.
Hock's lawyer said: "My client was having a nice time with a married couple and a lady friend and a group of very beautiful women, and these individuals were jealous, and they resorted to elementary-school tactics.
"My client is not Bruce Lee. These four guys are trust-fund babies who think the world is owed to them. They are like spoiled brats."
But Richard Golub, who is representing the prince and his friends, said, "It was a horrifying incident . . . It was entirely unprovoked."
Prince Pierre is the third in line to the throne of Monaco, following his mother Caroline and brother Andrea Albert. He is the grandson of Grace Kelly, the late American actress who married Prince Rainier of Monaco in 1956.
His father, Stefano, was Princess Caroline's second husband, and died in a boating accident when he was three.
Prince Pierre lives in Italy and works as a businessman.