This quote is deeply misleading. It's not completely clear but I think Rudy is talking about Biden, Trump and himself staking their reputations on the outcome of a fraud investigation.
Over the next 10 days, we get to see the machines that are crooked, the ballots that are fraudulent, and if we’re wrong, we will be made fools of. But if we’re right, a lot of them will go to jail. Let’s have trial by combat. I’m willing to stake my reputation, the President is willing to stake his reputation, on the fact that we’re going to find criminality there.Is Joe Biden willing to stake his reputation that there’s no crime there? No.
There is also a pause around the trial by combat comment that is not evident in the transcript so its probably worth listening to the speech to get the full context.
The RNC declared Trump to be the leader of their party after he told a crowd of armed terrorists that they should go to the Capitol and "save" the country from the politicians who were busy certifying the results of an election. They did so after that same crowd stormed the Capitol building, replaced the American flag with a Trump flag, and proudly declared to the cameras that they were there for a "revolution."
Kind of hard to know where the line is drawn between "declaring as your leader the man who advocates for a violent overthrow" and "advocating for a violent overthow."
> My goal is to cut government in half in twenty-five years, to get it down to the size where we can drown it in the bathtub. ~ Grover Norquest