Can't say I agree, and I suspect you probably don't agree with the implications of that definition either. As a hypothetical example, do you think any of the following aren't writing:

* a script which can represent taxes, histories, and religious texts but not the full range of verbal expression

* programming languages

* emojis

The first of these is an actual scholarly debate about whether Aztec script can be considered "full" writing or merely proto-writing.