The "media" in "social media" doesn't refer to image/video/audio, it refers to "the medium being used". Twitter/Blue Sky/etc are all social media. Read it like "a medium being used for social interaction".
OPs is closer to the truth; the shift from network -> media shows a useful distinction between what the focal point of activity is.
Note that "social" (as in social interaction with people you know) in "social networking" is a requirement, while it is not in "social media". You may as well call it "parasocial media" since that is the way most people use it most of the time.
Thus 'social media' is primarily based on content, while 'social networking' is primarily based on social connection and interaction.
If anything the terminology shift was the other way, we called forums and MySpace social media back then even though MySpace is called social networking now. "Networking" back then was pretty restricted to business / self-promotion oriented stuff like LinkedIn.
I was also there. We (ie the people I interacted with) called myspace social media and considered discussion forums to be a specialized subset of social media.
We also considered myspace to be a social network (due to the friend graph) while forums were not.
The chans were a weird almost edge case. I think they qualify as social media but the lack of persistent identities significantly changes the dynamics (obviously).
As far as I know chans are always considered "image boards" and they are usually distinct by the fact that the information is "pushed off" the board after a time or amount posted afterwards.
This delineation does not match the common usage of the terms as I understand them. If you want to talk about parasocial media then just use that term.
