The court heard that the party was being held at the luxury Snurridge Manor House near South Molton in north Devon to celebrate Mr King's pregnant mother's 40th birthday.
Witnesses said Dupree, a former boxing coach, was clenching a glass when he punched Mr King in the neck as the party began to quieten down at around 3am.
As Mr King fell to the floor clutching his wound, Dupree showed him no remorse, saying: "I've done him." He then left and walked home.
A terrified Mr King told shocked onlookers that he thought he was going to die as friends frantically called for help.
Mr King, who was from London, was taken to hospital but later died from his injuries.
Dupree, wearing spectacles, a white T-shirt and blue tracksuit bottoms, stood expressionless as the jury foreman announced his guilt.
It then emerged that Dupree had a long history of criminal convictions dating back to being a juvenile in the 1960s.
These include offences against the person, public order and possession of firearms and offensive weapons.
He has served sentences in borstal and prison, the court was told.
The judge also heard of the effect Mr King's death has had upon his mother, Lisa Wilson, and family in victim impact statements.
"Lisa Wilson describes the unbearable grief that the loss of her son has brought to her and the devastation it has caused the wider family," prosecutor Simon Laws QC said.
Adam Vaitilingam QC, defending, did not offer any personal mitigation on behalf of Dupree.
At the start of the trial, the prosecutor said Dupree "grossly over-reacted to a trivial dispute".
Mr Laws said: "There was simply no reason for Dupree to have used any force at all, still less the fatal force that he actually used.
"Mr King lost his life quite needlessly. His death was a product of Dupree's bad temper and his pride."
Dupree and Mr King were among around 30 people celebrating Ms Wilson's birthday at the manor house, which was owned by Dupree's sister.
Revellers said the party was "going well", with music, a buffet and karaoke.
But, as guests began to leave the party, witnesses said the atmosphere began to change.
Mr Laws told the court: "Dupree was behaving in a manner which was, at the very least, overbearing.
"Mr King intervened on behalf of a young girl that was bearing the brunt of the defendant's temper."
He said Mr King asked Dupree to leave the girl alone, prompting Dupree to say his relative should "respect his elders".
Dupree had apparently become angry that one girl had broken two glasses, and that the teenagers, who had been drinking, should have been in bed.
The defendant, who was stopped by police as he walked home from the party, initially said the incident had been an accident, and that it was a "family thing" that had got out of hand.
He later said his great-nephew had "offered him outside for a fight" before launching a pre-emptive attack on the 20-year-old.
Dupree told the court that he "could not remember" the details of the incident, including whether he was holding a wine glass at the time he lashed out.
"I became aware (of the seriousness of Mr King's injury) when I got to the hospital and I heard my niece (Mr King's mother) scream out: 'Oh, my boy, my baby boy'," he told jurors.
"Ryan was in an adjoining (hospital) room. When I heard my niece, I said: 'What's going on?'
"A policeman told me to be quiet, because they (Mr King's family) don't know we were there."
Dupree told jurors he did remember telling some children at the party to go to bed.
He said Mr King later challenged him, talking in a "sarcastic" manner before the 68-year-old admitted offering his young relative to "go outside", as though to fight.
Dupree said: "He (Mr King) said: 'Come on, then'. He took half a step towards me, I got up and hit him."
The defendant said he threw one punch, a right-arm hook, which he demonstrated to the jury.
Passing sentence, the judge said Dupree had killed Mr King because he had lost his temper with some of the youngsters at the party.
"You killed him in a fit of temper and annoyance because you were not getting the respect and deference you thought you deserved, first by a 13-year-old girl and second your great-nephew Ryan," the judge said.
"When he tried to intervene and calm the situation and calm you down, you became aggressive, abusive and violent.
"You thrust a wine glass into his neck which cut his jugular vein and in reality he bled to death on the floor of his grandmother's kitchen.
"The fact you killed him in front of the people that were there, particularly the young girls, is an aggravating feature of this case."
The judge said he accepted Dupree had not intended to kill Mr King but he had wanted to cause him "really serious harm" when he attacked him.
Following the verdict, Detective Inspector Dave Thorne, who led the investigation, said: "Justice has prevailed in this tragic case and Raymond Dupree has been convicted of murder.
"It was a needless attack which was unprovoked and undeserved with fatal consequences to Ryan King, a young man with his whole life ahead of him.
"Ryan was part of an extensive but close-knit family with many good friends and was liked by all.
"The trauma and loss that family and friends have experienced is beyond comprehension and although a conviction has been achieved, people will live with this loss for the rest of their lives.
"I would like to thank the prosecution team for their professionalism and the family for their calmness and resilience through this traumatic process."
Mr King's family did not wish to comment as they left court.