Many people would say going to wikipedia to learn about irony and then failing to learn about irony, is ironic. This is wrong. It only has one outcome. Irony does requires a "double audience" as the quote says, but that double audience is within the same person.
I think the clearest example of irony is Socrates, who used a rhetorical device in his argument against using rhetoric. The fact that this argument against rhetoric is taken as damning rhetoric is IRONIC because he uses rhetoric to make his point, thus BOTH making his point AND not making his point at the same time.
The more persuasive his arguments against rhetoric are, the more useful rhetorical devises are proven to be.
THIS IS IRONY.
I wish people would stop saying "isn't it ironic" about things which clearly aren't.