He isn't making the claim that it can encode more bits than the information theoretic maximum you suggest _on average_. On average his method is similar or wors

He isn't making the claim that it can encode more bits than the information theoretic maximum you suggest _on average_. On average his method is similar or worse than optimal. But some messages are effectively compressed in this encoding, and so more plaintext bits can be encoded. These better than average messages "borrow" bits from the worse than average messages, similar to how a compression algorithm works.