Vectors in the way he talks about in the beginning. With indices (and then extending to "In higher dimensions, vectors start to look more like functions!"). Of course if you use the general meaning of every word, vectors are functions and functions are vectors, and this article shouldn't then have anything interesting to talk about.
how the above result is useful
It doesn't seem useful at all to me, the examples in the article are not that interesting. On the contrary it is more confusing than anything to apply linear algebra to real valued functions.
