If an official commits treason in the U.S., can any political figure kill him without trial?

No. Political ination is not authorized for any purpose in the US law or practice. Treason is only punishable by death or life imprisonment after trial. And the constitutional definition of "treason" is limited to wartime, and only for specific crimes (no other crime or crimes constitute "treason"). Some people talk a lot of trash and nonsense, and use the word "treason" a little too loosely, and without understanding the legal definition of the word. Nor is there any provision in law or outside of self-appointed vigilantes who think they know more than the government who should be eliminated. This is the sort of thing of bad fiction and worse films or television writing.