Te Riini, who was standing outside the house, banged on the cracked bedroom window to try to make the couple stop arguing and broken glass spread into the room.
An enraged Akurangi charged out of the house and ran at his father-in-law, who was standing on a concrete patio, and pushed him.
Te Riini was thrown backwards, landed on his back and suffered a fractured neck with severe swelling to his spinal cord.
He died five days later in Middlemore Hospital after his life support was turned off.
Akurangi told police he was angry at Te Riini and as he ran at him, his leg struck a chair on the patio and he collided with the deceased "chest-to-chest", causing his father-in-law to be propelled backwards.
Crown prosecutor Duncan McWilliam told Justice Graham Lang that, despite the gravity of Akurangi's crime, the Crown did not oppose a sentence of home detention.
He noted Akurangi had a prior breach of home detention and community work but acknowledged that was some years ago and accepted some remorse had been shown.
Akurangi's lawyer Rachael Adams urged Justice Lang to impose a sentence of home detention, which she argued was the appropriate and least restrictive outcome.
Adams said her client had clearly not intended to cause the death of Te Riini and he was full of remorse and grief for what happened.
She said Akurangi's cultural background report made "very sad" reading as it detailed his "highly dysfunctional" childhood and an upbringing that was "brutal".
Adams said it was quite predictable that Akurangi had got involved in substance abuse and a gang lifestyle as a young man but he had turned his back on the gangs and overcome his P addiction and stopped drinking.
"Mr Akurangi is no longer the same man he was 20 years ago and he has taken considerable steps to change the direction of his life," she said.
Adams said Akurangi deeply regretted what happened that night and had demonstrated genuine remorse and a willingness to turn his life around.
"It's an understatement to say Mr Akurangi carries the burden of what he did that night very deeply and has been identified as being at serious risk of self-harm."
Adams said Akurangi also had poorly-controlled epilepsy and, along with mental health issues, that would add another hardship to his sentence if he was sent to jail.
Justice Lang acknowledged the grief of Te Riini''s "devastated" family members seated in the public gallery, including his widow and daughter, and many tears flowed.
"Nothing I can do can bring Jay back and this has been dreadful for you trying to cope with the loss of a loved one, and the sentence I impose won't bring closure for you."
Justice Lang said victim impact statements made harrowing reading but were measured, and all spoke of the devastation and deep feelings of loss.
"I extend my sympathies on behalf of the court to you at this terrible time," he said.
Justice Lang said Akurangi's cultural background report and the pre-sentence report did make sad reading but it was clear he had made a number of changes in his life.
He accepted Akurangi was genuinely remorseful and wanted to turn his life around.
Justice Lang said he was satisfied Akurangi's actions that night seemed to have been an "unfortunate aberration" and imposed eight months and two weeks' home detention.
But he warned Akurangi any breach of his sentence would see him sent to prison.
