Irony of the novel Tik-Tok
The novel overall is an ironic answer to the novel I, Robot, where robots are depicted as never harming humans and obeying the laws that prevent them to harm humans. Tik-Tok is an opposition to that and in the novel and even the writer of I, Robot and his laws are mentioned. Tik-Tok questions these laws as something that is not possible, that morality is something highly unlikely to be digitally engraved into a machine and it follows a robot that refuses to obey those laws.
Irony of the old man playing chess
Tik-Tok is drawn to the old rugged man playing the chess on the street. He even tries to talk to him about his troubles. Tik-Tok is baffled by the old man's chess playing skills and can't understand how he is only to able to beat him once in ten games in a row. Ironically, the old man is a fraud.
Irony of humans
No one seems to notice or doubt Tik-Tok's behavior because people want to believe that robots aren't a threat to humans. It is either this, or as it is shown in the ending chapters, people aren't that far off morally from Tik-Tok. Even after he confesses and tells his entire story they still want him to be the Vice President and he begins further planning the extinction of humans.