If everyone knows that the liar always lies, then can he effectively even lie? It’s like he speaks a language where everything means the opposite of what it means in English, and everyone understands this semantically inverted language. So then he might lie by just telling the truth.
That would only be true if the liar speaks in purely boolean statements. Many statements aren't invertible because the possibility space is larger than true or false.
The article even defines "liar" for you: "A liar is someone who only says false statements." It's not someone who is trying to maximally mislead.