It is only a chat platform and it predates the first social networks (which were explicitly called "social networks" back then). This is a bit of a pet peeve of mine, but I think people use the term "social network" way to much so that it doesn't even mean anything any more.

I don't know what the official ICQ client does today but back in the day it had more than just chats between people. It had file sharing, etc.

We associate other stuff like sharing and virality with social networks. Isn't the phone network just as much of a social network as ICQ?

I think party lines on the phone, yes.