This is to transmit confidential information without using encryption. Something I predict will be more and more needed, as democratic governments succumb into their autocratic temptations and attempt to ban encryption.
The secret message must be encrypted (ideally with just a one time pad to preserve the guarantees) or everyone could simply read it -- the paper assumes the model is public.
The technique lets you turn an encrypted message into the output of a sampled auto-regressive model in a way which is impossible for someone to distinguish from just running the model normally unless they have the private key, even if the attacker has the exact model you're using.