From the article: "[Alyx] had a crush on someone who was hearing impaired, so she taught Dog how to sign so she could practice. Something happened, maybe, the person is off fighting the Combine someplace else, but that's why she and Dog would start signing with each other when they wanted to communicate without making noise, or communicate without other people knowing ... It gave us the excuse to build the technology for signing."
DOG is a fucking robot! Why not just text it to him, or have Alyx use her magic sparkly wand that overrides all the Combine technology and is just a super convenient plot device all around?