Writing is using words on a page to tell information on some subject and activities which constitute writing are things like blogging, typing on you computer, even texting.
I cannot say that there is anything that is not writing because according to my definition of writing as long as there is words on a page it is writing .
I agree with most of what you are saying in this. Anything that is using words to communicate or express ideas or tell someone something should be constituted as writing, however there are somethings such as heiroglifics or cave art which are symbols that can constituted as writing as they too are expressing ideas and telling information to the next person to see them.
I agree with his examples of what activities include writing because all three of them are all ways that writing is the proper form of communication in that situation.
I disagree with his examples though because there are multiple activities that do not include writing like driving, playing sports, etc…