Intense footage from inside celebrity chef David Burke's Red Horse restaurant shows the wild altercation ... and the tension is so thick you could cut it with a knife.

The video picks up with a restaurant manager trying to calm down two parties at neighboring tables ... and a guy in a white shirt, who cops say ultimately gets cut by a knife, tells the other group, "You shouldn't be doing medication and drinking martinis."

You can hear the man continue to egg on the other table ... telling them, "Slow down on the old spirits, people."

A woman at the neighboring table tells the guy it was just an accident. The man in white motions to his dinner date as he responds, "An accident is why there's wine all over her back."

The argument continues as the man turns and faces a diner at the neighboring table and asks, "You got a knife in your hand?"

Instantly, the diner stands up ... and video appears to show him lunging at the man in white, grabbing him with his left hand, with the knife in his right hand.

The knife-wielding man -- wearing blue -- is easily thrown down on his keester, and folks rush over to break the two men up ... as shocked patrons shriek for someone to call the cops.

The Rumson Police Department says 75-year-old David Gulley of Palm Beach Shores, FL is the man in blue in the video ... and he's accused of pulling out a steak knife and lunging at the other man.

Police arrested Gulley for aggravated assault, possession of a weapon for an unlawful purpose, terroristic threats, disorderly conduct and simple assault ... and he's since been released from custody.

Cops also say the man in white's finger was cut in the incident ... but he refused treatment.