In communication, chatting over the internet is

Chatting over the internet is verbal communication, because it exchanges meaning through written words.

Verbal communication covers both spoken and written language, and typed chat is written language.

It is not non-verbal, since gestures and body cues are not the carrier here, words are.

Parallel communication is not a standard category that fits typed online conversation.

Grapevine communication is an informal organisational rumour channel, not defined by the internet medium.

Because words do the work, online chat sits within verbal communication.