Why isn't it? I posted status updates. I posted links to news articles. I posted links to pictures. I had direct message conversations and public conversations. I had a registered username. I had a biography.
Social communication has just evolved over the years. From Usenet to IRC to Forums to Friendstr and MySpace, it's all social.
About a decade ago I was interviewed for a social media manager role and said the same thing. They did not approve my take and I knew they would be horrible to work with. Their concept was that all social media started with Facebook and Twitter (but even Myspace or friendster, let alone icq or forums and they didn't know what Usenet was). I said "the Internet IS inherently social media no matter the silo" and I guess that went over the head.
i agree they're shades of the same thing, but i think 'media' implies the intent to publish (semi-)publicly, whereas chat messages are meant to be more ephemeral and shared with a limited group