The Ohio man was convicted last year of shooting Ronald Horton in the face the day after thanksgiving last year.
He entered a not guilty plea in January by reason of insanity but was found guilty after a one-day trial.
In a handwritten statement to police, Binkiewicz said Mr Horton pulled a gun on him first as he tried to leave the victim's house.
"I turned and started to follow him back through the kitchen to the back door," he wrote.
"At back door he stopped to let me go by to open back door to leave. I passed him then ... started to open back door. As I turned around to say goodbye to him I seen a gun in his right hand coming up at me.
"I grabbed his right wrist with my left hand ... At this point the gun went off in his hand."
On Saturday, Binkiewicz sat silently in the courtroom as Judge Michelle Miller handed down her sentence.
Binkiewicz's hands were shackled but his feet were not - local news reports suggest there were previous issues with swelling.
A short way outside the courtroom doors, he ran from the sheriff's deputy escorting him to the elevator and leapt to his death.
Jefferson County Sheriff Fred Abdalla said the deputy was holding Binkiewicz's shirt when he jumped.
"As soon as Binkiewicz started running, (the deputy) he was on him quick enough when he reached out, he had his shirt. It wasn't good enough, and if he held on to the shirt, most likely (the deputy) would have gone over with him."
Prosecutor Jane Hanlin told the media nobody thought Binkiewicz was capable of doing what he did.
"I don't think that anybody thought that this was going to happen today. Sometimes if we are aware something has happened in the past, or there have been those types of threats, then we are looking for that, we're going to be taking different action," she said.
"It really is just a heartbreaking day for everybody here because they're typically lots of people in the courthouse, there are criminal proceedings going on, a lot of activity at the courthouse.
"We are thankful that the deputy wasn't injured and we're actually thankful that nobody else was hurt as he went over that railing, that he didn't hurt or kill anybody else on the way down."
She said Jefferson County officials will be reviewing security in future as a result of Binkiewicz's death.
"I think we're going to look at everything. It is a terrible day for this to have happened and we will look at everything we can to make sure nothing like this ever happens again. He had his mind made up he was going to do this, and he succeeded."
Where to get help:
• Lifeline: 0800 543 354 (available 24/7)
• Suicide Crisis Helpline: 0508 828 865 (0508 TAUTOKO) (available 24/7)
• Youthline: 0800 376 633
• Kidsline: 0800 543 754 (available 24/7)
• Whatsup: 0800 942 8787 (1pm to 11pm)
• Depression helpline: 0800 111 757 (available 24/7)
• Rainbow Youth: (09) 376 4155
• Samaritans 0800 726 666
• If it is an emergency and you feel like you or someone else is at risk, call 111.