What can we do when our father is becoming narcissistic, bullying, argumentative, and prone to issuing ultimatums?

Since these are personality traits that have always been present it could be that he has reached an age where he can't be bothered hiding his true nature anymore. It could also be dementia is robbing him of his social filters and making him paranoid, especially since it is bad enough that he has chased off almost everyone in his life. How is his wife coping?
I'm not certain there is much you can do, especially since he has come to distrust everyone. You perhaps could write out your concerns and send them to his doctor to alert him to the changes you have seen in him.

You could call the area on aging and give them a heads up that he is becoming alienated from all who care for him. You could ask that they do a periodic wellness check. He's sure not to like that but it might help you keep up with him. They do not have to tell you anything but sometimes they do. Does your fathers wife have children? If so you might want to discuss with them so they can check on her. Should he have a reason to go to the ER or Into the hospital, you and the siblings should have a plan to try to have him evaluated at that time.
I would keep in touch with your step mother if possible. At 83 with the behavior you describe, something will happen. Be ready.

Thank you. His wife is very timid when the rest of us are around. He bullies her also. But, apparently, she nags him when they're alone. So he says, anyway. If I knew who his doctor was, that would be a great idea.

Thank you very much. I sincerely appreciate it. I'll do that.

If it's dementia, he may be incapable of recognizing that he's in trouble. The brain just won't allow it. It's called agnosia. I have observed where the patient runs everyone off, but, then when they really crash, it's a crisis. They can no longer function, confused and frightened. I'd let his wife know to call when that happens.