Great points. I wrote my comment in response to the article claiming to be an intuitive guide to linear algebra, not an intuitive guide to matrices. According to wikipedia:

Linear algebra is the branch of mathematics concerning linear equations, linear functions, and their representations in vector spaces through matrices. [0]

The Venn Diagram of Linear Algebra and Matrices definitely has a lot of non-overlap, of which your list covers some. This article should be renamed to be about matrices and not linear algebra, because it's not.

[0] https://en.wikipedia.org/wiki/Linear_algebra